1% 2% Testing file for REDUCE Special Functions Package 3% 4% Chris Cannam, ZIB Berlin 5% October 1992 -> Feb 1993 6% (only some of the time, of course) 7% 8% Corrections and comments to neun@sc.zib-berlin.de 9% 10 11 12on savesfs; 13 14 % just in case it's off for some reason 15 16off bfspace; 17 18 % to provide more similarity between runs 19 % with old & new bigfloats 20 21let {sinh (~x) => (exp(x) - exp (-x))/2 }; 22 23 24 % this will improve some results 25 26 27% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 28 29% 1. Bernoulli numbers 30 31% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 32 33 34off rounded; 35 36 37 38procedure do!*one!*bern(x); 39 write ("Bernoulli ", x, " is ", bernoulli x); 40 41 42do*one*bern 43 44 45do!*one!*bern(1); 46 47 48 - 1 49Bernoulli 1 is ------ 50 2 51 52do!*one!*bern(2); 53 54 55 1 56Bernoulli 2 is --- 57 6 58 59do!*one!*bern(3); 60 61 62Bernoulli 3 is 0 63 64do!*one!*bern(13); 65 66 67Bernoulli 13 is 0 68 69do!*one!*bern(14); 70 71 72 7 73Bernoulli 14 is --- 74 6 75 76do!*one!*bern(300); 77 78 79Bernoulli 300 is ( - 186387899520485901199504534184815606618219184663590593751\ 80 8715320655775958174360523134990756922303410810482600528769\ 81 4796420210012184158790061643029553704608291464348079647177\ 82 3719535693514415158342483315425004774743357558499902912677\ 83 5186293388721514970183351129809976971603227633930434923843\ 84 9848295803115933725653985747628800282891676355700124156069\ 85 41367995702212211519561707046505473575241)/866054419230 86 87do!*one!*bern(-2); 88 89 90Bernoulli -2 is bernoulli(-2) 91 92do!*one!*bern(0); 93 94 95Bernoulli 0 is 1 96 97 98for n := 2 step 2 until 100 do do!*one!*bern n; 99 100 101 1 102Bernoulli 2 is --- 103 6 104 105 - 1 106Bernoulli 4 is ------ 107 30 108 109 1 110Bernoulli 6 is ---- 111 42 112 113 - 1 114Bernoulli 8 is ------ 115 30 116 117 5 118Bernoulli 10 is ---- 119 66 120 121 - 691 122Bernoulli 12 is -------- 123 2730 124 125 7 126Bernoulli 14 is --- 127 6 128 129 - 3617 130Bernoulli 16 is --------- 131 510 132 133 43867 134Bernoulli 18 is ------- 135 798 136 137 - 174611 138Bernoulli 20 is ----------- 139 330 140 141 854513 142Bernoulli 22 is -------- 143 138 144 145 - 236364091 146Bernoulli 24 is -------------- 147 2730 148 149 8553103 150Bernoulli 26 is --------- 151 6 152 153 - 23749461029 154Bernoulli 28 is ---------------- 155 870 156 157 8615841276005 158Bernoulli 30 is --------------- 159 14322 160 161 - 7709321041217 162Bernoulli 32 is ------------------ 163 510 164 165 2577687858367 166Bernoulli 34 is --------------- 167 6 168 169 - 26315271553053477373 170Bernoulli 36 is ------------------------- 171 1919190 172 173 2929993913841559 174Bernoulli 38 is ------------------ 175 6 176 177 - 261082718496449122051 178Bernoulli 40 is -------------------------- 179 13530 180 181 1520097643918070802691 182Bernoulli 42 is ------------------------ 183 1806 184 185 - 27833269579301024235023 186Bernoulli 44 is ---------------------------- 187 690 188 189 596451111593912163277961 190Bernoulli 46 is -------------------------- 191 282 192 193 - 5609403368997817686249127547 194Bernoulli 48 is --------------------------------- 195 46410 196 197 495057205241079648212477525 198Bernoulli 50 is ----------------------------- 199 66 200 201 - 801165718135489957347924991853 202Bernoulli 52 is ----------------------------------- 203 1590 204 205 29149963634884862421418123812691 206Bernoulli 54 is ---------------------------------- 207 798 208 209 - 2479392929313226753685415739663229 210Bernoulli 56 is --------------------------------------- 211 870 212 213 84483613348880041862046775994036021 214Bernoulli 58 is ------------------------------------- 215 354 216 217 - 1215233140483755572040304994079820246041491 218Bernoulli 60 is ------------------------------------------------ 219 56786730 220 221 12300585434086858541953039857403386151 222Bernoulli 62 is ---------------------------------------- 223 6 224 225 - 106783830147866529886385444979142647942017 226Bernoulli 64 is ----------------------------------------------- 227 510 228 229 1472600022126335654051619428551932342241899101 230Bernoulli 66 is ------------------------------------------------ 231 64722 232 233 - 78773130858718728141909149208474606244347001 234Bernoulli 68 is ------------------------------------------------- 235 30 236 237 1505381347333367003803076567377857208511438160235 238Bernoulli 70 is --------------------------------------------------- 239 4686 240 241 - 5827954961669944110438277244641067365282488301844260429 242Bernoulli 72 is ------------------------------------------------------------ 243 140100870 244 245 34152417289221168014330073731472635186688307783087 246Bernoulli 74 is ---------------------------------------------------- 247 6 248 249 - 24655088825935372707687196040585199904365267828865801 250Bernoulli 76 is ---------------------------------------------------------- 251 30 252 253 414846365575400828295179035549542073492199375372400483487 254Bernoulli 78 is ----------------------------------------------------------- 255 3318 256 257Bernoulli 80 is ( - 4603784299479457646935574969019046849794257872751288919656\ 258 867)/230010 259 260 1677014149185145836823154509786269900207736027570253414881613 261Bernoulli 82 is --------------------------------------------------------------- 262 498 263 264Bernoulli 84 is ( - 2024576195935290360231131160111731009989917391198090877281\ 265 083932477)/3404310 266 267Bernoulli 86 is 660714619417678653573847847426261496277830686653388931761996983/ 268 6 269 270Bernoulli 88 is ( - 1311426488674017507995511424019311843345750275572028644296\ 271 919890574047)/61410 272 273Bernoulli 90 is 11790572790210827998841233512492150837752549496696471162315452\ 274 15727922535/272118 275 276Bernoulli 92 is ( - 1295585948207537527989427828538576749659341483719435143023\ 277 316326829946247)/1410 278 279Bernoulli 94 is 12208138065797444696073016794132012039585084152026966214362151\ 280 05284649447/6 281 282Bernoulli 96 is ( - 2116004495972665130975977281098242336730439543890602341506\ 283 38733420050668349987259)/4501770 284 285Bernoulli 98 is 67908260672905495624051117546403605607342195728504487509073961\ 286 249992947058239/6 287 288Bernoulli 100 is ( - 945980378191221252952274330694937218727028415330669361333\ 289 85696204311395415197247711)/33330 290 291 292on rounded; 293 294 295precision 100; 296 297 29812 299 300 301do!*one!*bern(1); 302 303 304Bernoulli 1 is - 0.5 305 306do!*one!*bern(2); 307 308 309Bernoulli 2 is 310 311 0.1666666666666666666666666666666666666666666666666666666666666\ 312 666666666666666666666666666666666666667 313 314do!*one!*bern(3); 315 316 317Bernoulli 3 is 0 318 319do!*one!*bern(13); 320 321 322Bernoulli 13 is 0 323 324do!*one!*bern(14); 325 326 327Bernoulli 14 is 328 329 1.166666666666666666666666666666666666666666666666666666666666\ 330 666666666666666666666666666666666666667 331 332do!*one!*bern(300); 333 334 335Bernoulli 300 is - 336 337 2.15214997327998682971981737675608819857345657278380670184934\ 338 3925846796995824343474766557085976828531e+375 339 340do!*one!*bern(-2); 341 342 343Bernoulli -2 is bernoulli(-2) 344 345do!*one!*bern(0); 346 347 348Bernoulli 0 is 1 349 350do!*one!*bern(38); 351 352 353Bernoulli 38 is 354 355 4.883323189735931666666666666666666666666666666666666666666666\ 356 666666666666666666666666666666666666667e+14 357 358do!*one!*bern(400); 359 360 361Bernoulli 400 is - 362 363 6.84694485580645336061625858231088359767823009718062574241478\ 364 1150311357197834589950328990573681886442e+549 365 366 367 368% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 369 370% 2. Gamma function 371 372% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 373 374 375on rounded; 376 377 378off complex; 379 380 381precision 40; 382 383 384100 385 386 387algebraic procedure wg(x); 388 write ("gamma (", x, ") ==> ", gamma x); 389 390 391wg 392 393 394algebraic procedure wp(x); 395 write ("-- precision ", x, ", from ", precision(x)); 396 397 398wp 399 400 401wg (1/2); 402 403 404gamma (0.5) ==> 1.772453850905516027298167483341145182798 405 406wg (3/2); 407 408 409gamma (1.5) ==> 0.8862269254527580136490837416705725913988 410 411 412write ("sqrt(pi)/2 ==> ", sqrt(pi)/2); 413 414 415sqrt(pi)/2 ==> 0.8862269254527580136490837416705725913988 416 417 418wp(10); 419 420 421-- precision 10, from 40 422 423 424for x := 0 step 5 until 100 do 425 << wg (1 + x/1000); 426 wg (-1 - x/13); 427 wp (8+floor(x/4)) >>; 428 429 430gamma (1) ==> 1 431 432gamma (-1) ==> gamma(-1) 433 434-- precision 8, from 10 435 436gamma (1.005) ==> 0.99713854 437 438gamma ( - 1.3846154) ==> 2.7320314 439 440-- precision 9, from 8 441 442gamma (1.01) ==> 0.994325851 443 444gamma ( - 1.76923077) ==> 2.89933597 445 446-- precision 10, from 9 447 448gamma (1.015) ==> 0.9915612888 449 450gamma ( - 2.153846154) ==> - 2.919307224 451 452-- precision 11, from 10 453 454gamma (1.02) ==> 0.98884420326 455 456gamma ( - 2.5384615385) ==> - 0.91247160689 457 458-- precision 13, from 11 459 460gamma (1.025) ==> 0.9861739631483 461 462gamma ( - 2.923076923077) ==> - 2.407817725014 463 464-- precision 14, from 13 465 466gamma (1.03) ==> 0.98354995055382 467 468gamma ( - 3.3076923076923) ==> 0.42665848359037 469 470-- precision 15, from 14 471 472gamma (1.035) ==> 0.980971560550586 473 474gamma ( - 3.69230769230769) ==> 0.250121998146955 475 476-- precision 16, from 15 477 478gamma (1.04) ==> 0.9784382009142447 479 480gamma ( - 4.076923076923077) ==> - 0.4868211588210416 481 482-- precision 18, from 16 483 484gamma (1.045) ==> 0.975949291822951489 485 486gamma ( - 4.46153846153846154) ==> - 0.064315864992688343 487 488-- precision 19, from 18 489 490gamma (1.05) ==> 0.9735042655627756432 491 492gamma ( - 4.846153846153846154) ==> - 0.07308480130893001268 493 494-- precision 20, from 19 495 496gamma (1.055) ==> 0.9711025662416699039 497 498gamma ( - 5.2307692307692307692) ==> 0.026504298643014994546 499 500-- precision 21, from 20 501 502gamma (1.06) ==> 0.968743649511638364209 503 504gamma ( - 5.61538461538461538462) ==> 0.00947958151841097406813 505 506-- precision 23, from 21 507 508gamma (1.065) ==> 0.96642698229883993296188 509 510gamma (-6) ==> gamma(-6) 511 512-- precision 24, from 23 513 514gamma (1.07) ==> 0.964152042541366448869499 515 516gamma ( - 6.38461538461538461538462) ==> - 0.00224562428754660955672785 517 518-- precision 25, from 24 519 520gamma (1.075) ==> 0.9619183189344448686422338 521 522gamma ( - 6.769230769230769230769231) ==> - 0.0014913552210721080976799 523 524-- precision 26, from 25 525 526gamma (1.08) ==> 0.95972531068282223532653464 527 528gamma ( - 7.1538461538461538461538462) ==> 0.0009821350464726696000373901 529 530-- precision 28, from 26 531 532gamma (1.085) ==> 0.9575725272601010524841387298 533 534gamma ( - 7.538461538461538461538461538) ==> 0.0002081367552774423831456972591 535 536-- precision 29, from 28 537 538gamma (1.09) ==> 0.95545948817480124076971838245 539 540gamma ( - 7.9230769230769230769230769231) ==> 541 5420.00038372470359721945415080451977 543 544-- precision 30, from 29 545 546gamma (1.095) ==> 0.95338572274293305256571929565 547 548gamma ( - 8.30769230769230769230769230769) ==> 549 550 - 0.0000487302698231202992921248405302 551 552-- precision 31, from 30 553 554gamma (1.1) ==> 0.9513507698668731836292487177265 555 556gamma ( - 8.692307692307692307692307692308) ==> 557 558 - 0.00002092711689267207910068115762837 559 560-- precision 33, from 31 561 562 563wg(1/1000000003); 564 565 566gamma (0.000000000999999997000000008999999973) ==> 567 5681.00000000242278433608752313084681e+9 569 570 571off rounded; 572 573 574 575gamma(17/2); 576 577 578 2027025*sqrt(pi) 579------------------ 580 256 581 582gamma(-17/2); 583 584 585 - 512*pi 586------------------- 587 34459425*sqrt(pi) 588 589gamma(4); 590 591 5926 593 594gamma(0); 595 596 597gamma(0) 598 599gamma(-4); 600 601 602gamma(-4) 603 604gamma(-17/3); 605 606 607 6*pi 608------------------------ 609 17 610 17*sqrt(3)*gamma(----) 611 3 612 613 614p := gamma(x**2) * gamma(x-y**gamma(y)) - (1/(gamma(4*(x-y)))); 615 616 617 2 gamma(y) 618 gamma(x )*gamma( - y + x)*gamma(4*x - 4*y) - 1 619p := -------------------------------------------------------- 620 gamma(4*x - 4*y) 621 622y := 1/4; 623 624 625 1 626y := --- 627 4 628 629p; 630 631 632 2 1 gamma(1/4) 633 gamma(x )*gamma( - (---) + x)*gamma(4*x - 1) - 1 634 4 635------------------------------------------------------------ 636 gamma(4*x - 1) 637 638x := 3; 639 640 641x := 3 642 643p; 644 645 646 1 gamma(1/4) 647 146313216000*gamma( - (---) + 3) - 1 648 4 649------------------------------------------------ 650 3628800 651 652y := -3/8; 653 654 655 - 3 656y := ------ 657 8 658 659p; 660 661 662(128*(2490343877896875*sqrt(pi) 663 664 - 3 (8*pi)/(3*gamma(3/8)*sin((3*pi)/8)) 665 3*(------) - 1 666 8 667 *gamma(---------------------------------------------------) - 64))/( 668 - 3 (8*pi)/(3*gamma(3/8)*sin((3*pi)/8)) 669 (------) 670 8 671 672 7905853580625*sqrt(pi)) 673 674 675on rounded, complex; 676 677 678*** Domain mode rounded changed to complex-rounded 679 680precision 50; 681 682 68333 684 685 686p; 687 688 689 - 0.00000000058461000084165968732153392127582134179078414159599 690 691 + 3.7721251013859508830301986850709684723938237902095e-60*i 692 693 694off rounded, complex; 695 696 697*** Domain mode complex-rounded changed to complex 698 699clear y; 700 701 702 703p; 704 705 706 gamma(y) 707 40320*gamma( - y + 3)*gamma( - 4*y + 12) - 1 708------------------------------------------------------ 709 gamma( - 4*y + 12) 710 711 712 713 714% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 715 716% 3. Beta function. Not very interesting 717 718% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 719 720 721algebraic procedure do!*one!*beta(x,y); 722 write ("Beta (", x, ",", y, ") = ", beta(x,y)); 723 724 725do*one*beta 726 727 728do!*one!*beta(0,1); 729 730 731Beta (0,1) = beta(0,1) 732 733do!*one!*beta(2,-3); 734 735 736Beta (2,-3) = beta(2,-3) 737 738do!*one!*beta(3,2); 739 740 741 1 742Beta (3,2) = ---- 743 12 744 745do!*one!*beta(a+b,(c+d)**(b-a)); 746 747 748 b 749 (c + d) 750 gamma(a + b)*gamma(----------) 751 b a 752 (c + d) (c + d) 753Beta (a + b,----------) = --------------------------------------------- 754 a a a b 755 (c + d) (c + d) *a + (c + d) *b + (c + d) 756 gamma(------------------------------------) 757 a 758 (c + d) 759 760do!*one!*beta(-3,4); 761 762 763Beta (-3,4) = beta(-3,4) 764 765do!*one!*beta(-3,2); 766 767 768Beta (-3,2) = beta(-3,2) 769 770do!*one!*beta(-3,-7.5); 771 772 773 - 15 - 15 774Beta (-3,-------) = beta(-3,-------) 775 2 2 776 777do!*one!*beta((pi * 10), exp(5)); 778 779 780 5 781 5 gamma(e )*gamma(10*pi) 782Beta (10*pi,e ) = ------------------------ 783 5 784 gamma(e + 10*pi) 785 786 787on rounded; 788 789 790precision 30; 791 792 79350 794 795 796do!*one!*beta(0,1); 797 798 799Beta (0,1) = beta(0,1) 800 801do!*one!*beta(2,-3); 802 803 804Beta (2,-3) = beta(2,-3) 805 806do!*one!*beta(3,2); 807 808 809Beta (3,2) = 0.0833333333333333333333333333333 810 811do!*one!*beta(a+b,(c+d)**(b-a)); 812 813 814 b 815 (c + d) 816 gamma(a + b)*gamma(----------) 817 b a 818 (c + d) (c + d) 819Beta (a + b,----------) = --------------------------------------------- 820 a a a b 821 (c + d) (c + d) *a + (c + d) *b + (c + d) 822 gamma(------------------------------------) 823 a 824 (c + d) 825 826do!*one!*beta(-3,4); 827 828 829Beta (-3,4) = beta(-3,4) 830 831do!*one!*beta(-3,2); 832 833 834Beta (-3,2) = beta(-3,2) 835 836do!*one!*beta(-3,-7.5); 837 838 839Beta (-3, - 7.5) = beta(-3, - 7.5) 840 841do!*one!*beta((pi * 10), exp(5)); 842 843 844Beta (31.4159265358979323846264338328,148.413159102576603421115580041) = 845 8463.26162024071771351768890966259e-37 847 848 849 850 851% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 852 853% 4. Pochhammer notation 854 855% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 856 857 858off rounded; 859 860 861 862Pochhammer(4,5); 863 864 8656720 866 867Pochhammer(-4,5); 868 869 8700 871 872Pochhammer(4,-5); 873 874 875pochhammer(4,-5) 876 877Pochhammer(-4,-5); 878 879 880 - 1 881------- 882 15120 883 884Pochhammer(17/2,12); 885 886 887 157783444591397625 888-------------------- 889 4096 890 891Pochhammer(-17/2,12); 892 893 894 - 516891375 895-------------- 896 4096 897 898Pochhammer(1/3,14)*Pochhammer(2/3,15); 899 900 901 148260333813553014031851192320000000 902-------------------------------------- 903 68630377364883 904 905 906q := Pochhammer(1/5,11)*Pochhammer(2/5,11)*Pochhammer(3/5,11)* 907 Pochhammer(1-1/5,11)*Pochhammer(1,11)*Pochhammer(6/5,11)* 908 Pochhammer(70/50,11)*Pochhammer(8/5,11)*Pochhammer(9/5,11); 909 910 911q := 3083594385972516709231715156294765932567301688416624945842705314534752626\ 912 0421323040989302952930905614937458388095527696384131072/12924697071141057\ 913 41986576081359316958696581423282623291015625 914 915 916on complex; 917 918 919 920Pochhammer(a+b*i,c)*Pochhammer(a-b*i,c); 921 922 923pochhammer(a - i*b,c)*pochhammer(a + i*b,c) 924 925 926a := 2; 927 928 929a := 2 930 931b := 3; 932 933 934b := 3 935 936c := 5; 937 938 939c := 5 940 941 942Pochhammer(a+b*i,c)*Pochhammer(a-b*i,c); 943 944 9458950500 946 947 948off complex; 949 950 951on rounded; 952 953 954 955Pochhammer(1/5,11)*Pochhammer(2/5,11)*Pochhammer(3/5,11)* 956 Pochhammer(1-1/5,11)*Pochhammer(1,11)*Pochhammer(6/5,11)* 957 Pochhammer(70/50,11)*Pochhammer(8/5,11)*Pochhammer(9/5,11); 958 959 9602.38581559706937212593793381562e+67 961 962 963q; 964 965 9662.38581559706937212593793381562e+67 967 968 969Pochhammer(pi,floor (pi**8)); 970 971 9722.47253079057195612235973919163e+33625 973 974Pochhammer(-pi,floor (pi**7)); 975 976 9775.91750008101140123889628058136e+9185 978 979Pochhammer(1.5,floor (pi**8)); 980 981 9821.88808885937650373473836451368e+33619 983 984 985 986 987% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 988 989% 5. Digamma function 990 991% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 992 993 994procedure do!*one!*psi(x); 995 << precision (precision(0) + 4)$ 996 write("Psi of ", x, " is ", psi(x) ) >> ; 997 998 999do*one*psi 1000 1001 1002clear x, y; 1003 1004 1005 1006z := x * ((x+y)**2 + (x**y)); 1007 1008 1009 y 2 2 1010z := x*(x + x + 2*x*y + y ) 1011 1012 1013off rounded; 1014 1015 1016 1017do!*one!*psi(3); 1018 1019 1020 - 2*euler_gamma + 3 1021Psi of 3 is ---------------------- 1022 2 1023 1024do!*one!*psi(pi); 1025 1026 1027Psi of pi is psi(pi) 1028 1029do!*one!*psi(1.005); 1030 1031 1032 201 1 1033Psi of ----- is psi(-----) + 200 1034 200 200 1035 1036do!*one!*psi(1.995); 1037 1038 1039 pi 1 1040 199*cot(-----)*pi + 199*psi(-----) + 200 1041 399 200 200 1042Psi of ----- is ------------------------------------------ 1043 200 199 1044 1045do!*one!*psi(74); 1046 1047 1048Psi of 74 is ( - 136851726813476721146087646859200*euler_gamma 1049 1050 + 667084944417653637854891458725877)/13685172681347672114608764\ 1051 6859200 1052 1053do!*one!*psi(-1/2); 1054 1055 1056 - 1 1057Psi of ------ is - 2*log(2) - euler_gamma + 2 1058 2 1059 1060do!*one!*psi(-3); 1061 1062 1063 1064***** Psi undefined for nonpositive integer argument -3 1065 1066do!*one!*psi(z); 1067 1068 1069 y 2 2 y 3 2 2 1070Psi of x*(x + x + 2*x*y + y ) is psi(x *x + x + 2*x *y + x*y ) 1071 1072 1073on rounded; 1074 1075 1076precision 100; 1077 1078 107962 1080 1081 1082do!*one!*psi(3); 1083 1084 1085Psi of 3 is 1086 1087 0.9227843350984671393934879099175975689578406640600764011942327651\ 1088 1513227322233532906305293670825325048537 1089 1090do!*one!*psi(pi); 1091 1092 1093Psi of 1094 1095 3.141592653589793238462643383279502884197169399375105820974944592307816\ 1096 40628620899862803482534211706798214809 is 1097 10980.9772133079420067332920694864061823436408346099943256380095232865318105924777\ 109914131730207565436292873435576949 1100 1101do!*one!*psi(1.005); 1102 1103 1104Psi of 1.005 is - 1105 1106 0.569020911344382831688295690950028809267968870263469094699243\ 1107 7771372094405771031990077045450115105840960011306543 1108 1109do!*one!*psi(1.995); 1110 1111 1112Psi of 1.995 is 1113 1114 0.419554603028108628651620272287243954692129976503405961275768\ 1115 00237211077024989654159358528162438486780461247996589393 1116 1117do!*one!*psi(74); 1118 1119 1120Psi of 74 is 1121 1122 4.297293118804667639106350362560367137919643935000983615964648570\ 1123 79142072638532815275329153012799334519059885201047316254 1124 1125do!*one!*psi(-1/2); 1126 1127 1128Psi of - 0.5 is 1129 1130 0.03648997397857652055902366700124443280684039533956589295287\ 1131 2746128345029282945897851326282715415875401365590709051546051\ 1132 66846 1133 1134do!*one!*psi(-3); 1135 1136 1137 1138***** Psi undefined for nonpositive integer argument -3 1139 1140do!*one!*psi(z); 1141 1142 1143 y 2 2 y 3 2 2 1144Psi of x*(x + x + 2*x*y + y ) is psi(x *x + x + 2*x *y + x*y ) 1145 1146 1147precision 15; 1148 1149 1150132 1151 1152 1153x := 8/3; 1154 1155 1156x := 2.66666666666667 1157 1158y := 7/1000; 1159 1160 1161y := 0.007 1162 1163do!*one!*psi(z); 1164 1165 1166Psi of 21.74768766103287773 is 3.056340330052438423 1167 1168 1169on complex; 1170 1171 1172*** Domain mode rounded changed to complex-rounded 1173 1174 1175array psicomptest(10); 1176 1177 1178 1179psicomptest(1) := -13.0 + 2.0i; 1180 1181 1182psicomptest(1) := - 13.0 + 2.0*i 1183 1184psicomptest(2) := -9.5; 1185 1186 1187psicomptest(2) := - 9.5 1188 1189psicomptest(3) := -3.0 + i; 1190 1191 1192psicomptest(3) := - 3.0 + i 1193 1194psicomptest(4) := 8.0i; 1195 1196 1197psicomptest(4) := 8.0*i 1198 1199psicomptest(5) := 3.0; 1200 1201 1202psicomptest(5) := 3.0 1203 1204psicomptest(6) := 4.0 + 2.0i; 1205 1206 1207psicomptest(6) := 4.0 + 2.0*i 1208 1209psicomptest(7) := 7.0 + 4.0i; 1210 1211 1212psicomptest(7) := 7.0 + 4.0*i 1213 1214psicomptest(8) := 9.0 + 16.0i; 1215 1216 1217psicomptest(8) := 9.0 + 16.0*i 1218 1219psicomptest(9) := 10.0; 1220 1221 1222psicomptest(9) := 10.0 1223 1224psicomptest(10) := 15.0 + 5.0i; 1225 1226 1227psicomptest(10) := 15.0 + 5.0*i 1228 1229 1230for j:=1:10 do do!*one!*psi(psicomptest(j)); 1231 1232 1233Psi of - 13.0 + 2.0*i is 2.6137588586149231277909 + 2.9946009556428566351564*i 1234 1235Psi of - 9.5 is 2.30300103429768637527259355 1236 1237Psi of - 3.0 + i is 1.294650320622476977271878482722 1238 1239 + 2.87667404746858117413405079475*i 1240 1241Psi of 8.0*i is 2.080745674911800978012091156263302 1242 1243 + 1.6332963267948966192317863440681425*i 1244 1245Psi of 3.0 is 0.922784335098467139393487909917597568958 1246 1247Psi of 4.0 + 2.0*i is 1.395360746143208295887639101232315589394657 1248 1249 + 0.516961128796076382232241496006733373069544*i 1250 1251Psi of 7.0 + 4.0*i is 2.0326956522302214192655943142503615623915246486 1252 1253 + 0.5510181566532114322789718358305813971403337745*i 1254 1255Psi of 9.0 + 16.0*i is 2.89681672499674156396524701196330813055662505786883 1256 1257 + 1.08235712929483567733811718225816618166171737283367*i 1258 1259Psi of 10.0 is 2.251752589066721107647456163885851537211808918028330369 1260 1261Psi of 15.0 + 5.0*i is 1262 12632.7304638296862949658807696179355434065486393774434862562913 1264 1265 + 0.3319504266337825064013487331466704838924601236522898251895*i 1266 1267 1268for j:=1:10 do do!*one!*psi(conj(psicomptest(j))); 1269 1270 1271Psi of - 13.0 - 2.0*i is 1272 12732.61375885861492312779092681414576935243927815653319886872004667 1274 1275 - 2.99460095564285663515635556968177810390527354210169915597435706*i 1276 1277Psi of - 9.5 is 1278 1279 2.30300103429768637527259355084976605222629263212926398296056\ 1280 0277036 1281 1282Psi of - 3.0 - i is 1283 12841.2946503206224769772718784827219107224762629717635416232329897241189051 1285 1286 - 2.8766740474685811741340507947500004904456562664038166655750624843901542*i 1287 1288Psi of - 8.0*i is 1289 1290 2.080745674911800978012091156263301960447423157094657043233\ 1291 56772730687510837 - 1292 1293 1.633296326794896619231786344068142496793658097596197866746\ 1294 28197612585099252*i 1295 1296Psi of 3.0 is 1297 1298 0.92278433509846713939348790991759756895784066406007640119423276\ 1299 51151322732223353 1300 1301Psi of 4.0 - 2.0*i is 1302 13031.3953607461432082958876391012323155893946567716670922275697526053560369304559\ 1304129117 - 1305 13060.5169611287960763822322414960067333730695439777431470516513256070610078161450\ 13076425866*i 1308 1309Psi of 7.0 - 4.0*i is 1310 13112.0326956522302214192655943142503615623915246486036687439734425046244698504734\ 13121034449618 - 1313 13140.5510181566532114322789718358305813971403337745049891709724778015097808994965\ 131580820485152*i 1316 1317Psi of 9.0 - 16.0*i is 1318 13192.8968167249967415639652470119633081305566250578688281426281739736662826184456\ 132017485762055843 - 1321 13221.0823571292948356773381171822581661816617173728336735134819382305761766533865\ 132322373036427982*i 1324 1325Psi of 10.0 is 1326 1327 2.2517525890667211076474561638858515372118089180283303694482010\ 1328 190833862414763035830313069049622 1329 1330Psi of 15.0 - 5.0*i is 1331 13322.7304638296862949658807696179355434065486393774434862562913209669772515134843\ 13332633413224249878816897 - 1334 13350.3319504266337825064013487331466704838924601236522898251895017179559937376738\ 133655349668081047744811948*i 1337 1338 1339off complex, rounded; 1340 1341 1342*** Domain mode complex-rounded changed to rounded 1343 1344 1345clear x, y; 1346 1347 1348 1349df(psi(z), x); 1350 1351 1352 y 3 2 2 y y 2 2 1353polygamma(1,x *x + x + 2*x *y + x*y )*(x *y + x + 3*x + 4*x*y + y ) 1354 1355df(df(psi(z), y),x); 1356 1357 1358 2*y y 3 2 2 1359x *log(x)*polygamma(2,x *x + x + 2*x *y + x*y )*x*y 1360 1361 2*y y 3 2 2 1362 + x *log(x)*polygamma(2,x *x + x + 2*x *y + x*y )*x 1363 1364 y y 3 2 2 3 1365 + 3*x *log(x)*polygamma(2,x *x + x + 2*x *y + x*y )*x 1366 1367 y y 3 2 2 2 1368 + 4*x *log(x)*polygamma(2,x *x + x + 2*x *y + x*y )*x *y 1369 1370 y y 3 2 2 2 1371 + x *log(x)*polygamma(2,x *x + x + 2*x *y + x*y )*x*y 1372 1373 y y 3 2 2 1374 + x *log(x)*polygamma(1,x *x + x + 2*x *y + x*y )*y 1375 1376 y y 3 2 2 1377 + x *log(x)*polygamma(1,x *x + x + 2*x *y + x*y ) 1378 1379 y y 3 2 2 2 1380 + 2*x *polygamma(2,x *x + x + 2*x *y + x*y )*x *y 1381 1382 y y 3 2 2 2 1383 + 2*x *polygamma(2,x *x + x + 2*x *y + x*y )*x 1384 1385 y y 3 2 2 2 1386 + 2*x *polygamma(2,x *x + x + 2*x *y + x*y )*x*y 1387 1388 y y 3 2 2 1389 + 2*x *polygamma(2,x *x + x + 2*x *y + x*y )*x*y 1390 1391 y y 3 2 2 1392 + x *polygamma(1,x *x + x + 2*x *y + x*y ) 1393 1394 y 3 2 2 4 1395 + 6*polygamma(2,x *x + x + 2*x *y + x*y )*x 1396 1397 y 3 2 2 3 1398 + 14*polygamma(2,x *x + x + 2*x *y + x*y )*x *y 1399 1400 y 3 2 2 2 2 1401 + 10*polygamma(2,x *x + x + 2*x *y + x*y )*x *y 1402 1403 y 3 2 2 3 1404 + 2*polygamma(2,x *x + x + 2*x *y + x*y )*x*y 1405 1406 y 3 2 2 1407 + 4*polygamma(1,x *x + x + 2*x *y + x*y )*x 1408 1409 y 3 2 2 1410 + 2*polygamma(1,x *x + x + 2*x *y + x*y )*y 1411 1412int(psi(x), x); 1413 1414 1415log(gamma(x)) 1416 1417 1418on rounded; 1419 1420 1421 1422for k := 1 step 0.1 until 2 do do!*one!*psi(k); 1423 1424 1425Psi of 1 is - 1426 1427 0.5772156649015328606065120900824024310421593359399235988057672348\ 1428 848677267776646709369470632917467495146 1429 1430Psi of 1.1 is - 1431 1432 0.42375494041107679516821621901002540429164256244418892032639208\ 1433 410886791088152627023153983491219927980824243 1434 1435Psi of 1436 1437 1.200000000000000000000000000000000000000000000000000000000000000000000\ 1438 0000000000000000000000000000000000000436 is - 1439 14400.2890398965921882955472079624499521048255882742066428101758586641916247540916\ 144119652546577824319570362412407865259 1442 1443Psi of 1444 1445 1.300000000000000000000000000000000000000000000000000000000000000000000\ 1446 000000000000000000000000000000000000043598847 is - 1447 14480.1691908888667996556311611740386482662045749550711687623315864179308303857025\ 1449770257187015968591396298192251105235858 1450 1451Psi of 1452 1453 1.400000000000000000000000000000000000000000000000000000000000000000000\ 1454 0000000000000000000000000000000000000435988468871 is - 1455 14560.0613845445851161457306754820475284558263610965108101572339536752126110429305\ 145741383972160692353613817412775940509279641163 1458 1459Psi of 1460 1461 1.500000000000000000000000000000000000000000000000000000000000000000000\ 1462 00000000000000000000000000000000000004359884688711001 is 1463 14640.0364899739785765205590236670012444328068403953395658929528727461283450292829\ 14654589785132628271541587540136563146534955733265 1466 1467Psi of 1468 1469 1.600000000000000000000000000000000000000000000000000000000000000000000\ 1470 000000000000000000000000000000000000043598846887110012947 is 1471 14720.1260474527734762519060027178604347251561324119770594583999814034054978254255\ 1473642005933241989468878465660903942111555360670073983 1474 1475Psi of 1476 1477 1.700000000000000000000000000000000000000000000000000000000000000000000\ 1478 0000000000000000000000000000000000000435988468871100129469698 is 1479 14800.2085478748734939566799641840099706284504372410359405588951627233510439957197\ 14811888196195835704807678107428159405980321416315399468575 1482 1483Psi of 1484 1485 1.800000000000000000000000000000000000000000000000000000000000000000000\ 1486 0000000000000000000000000000000000000435988468871100129469697747 is 1487 14880.2849914332938615406087023668431645803658395103047771708901892057550387926143\ 148915995693623340760077947867402943634838596190123409034342599 1490 1491Psi of 1492 1493 1.900000000000000000000000000000000000000000000000000000000000000000000\ 1494 000000000000000000000000000000000000043598846887110012946969774698648 is 1495 14960.3561841611640597192247270839286155915181509595109651018840831788470124953308\ 149795055258791830992043449174689987285634836913342490624091145471 1498 1499 1500off rounded; 1501 1502 1503 1504% PSI_SIMP.TST F.J.Wright, 2 July 1993 1505 1506on evallhseqp; 1507 1508 1509factor psi; 1510 1511 on rat, intstr, div; 1512 1513 % for neater output 1514% Do not try using "off mcd"! 1515 1516psi(x+m) - psi(x+m-1) = 1/(x+m-1); 1517 1518 1519 1 1 1520-----------=----------- 1521 m + x - 1 m + x - 1 1522 1523psi(x+2) - psi(x+1) + 2*psi(x) = 1/(x+1) + 2*psi(x); 1524 1525 1526 1 1 15272*psi(x) + -------=2*psi(x) + ------- 1528 x + 1 x + 1 1529 1530psi(x+2) + 3*psi(x) = 4*psi(x) + 1/x + 1/(x+1); 1531 1532 1533 -1 -1 1534 x + 2 x + 2 15354*psi(x) + ---------=4*psi(x) + --------- 1536 x + 1 x + 1 1537 1538 1539psi(x + 1) = psi(x) + 1/x; 1540 1541 1542 -1 -1 1543psi(x) + x =psi(x) + x 1544 1545psi(x + 3/2) = psi(x + 1/2) + 1/(x + 1/2); 1546 1547 1548 1 2 1 2 1549psi(x + ---) + ---------=psi(x + ---) + --------- 1550 2 2*x + 1 2 2*x + 1 1551 1552psi(x - 1/2) = psi(x + 1/2) - 1/(x - 1/2); 1553 1554 1555 1 2 1 2 1556psi(x + ---) - ---------=psi(x + ---) - --------- 1557 2 2*x - 1 2 2*x - 1 1558 1559psi((x + 3a)/a); 1560 1561 1562 -1 1563 1 2*(3*x + 8*x + 12) 1564psi(---*x) + ---------------------- 1565 2 2 1566 x + 6*x + 8 1567 psi(x/y + 3); 1568 1569 1570 -1 2 1571 -1 y*(3*x + 2*x *y + 6*y) 1572psi(x*y ) + -------------------------- 1573 2 2 1574 x + 3*x*y + 2*y 1575 1576 1577off rat, intstr, div; 1578 1579 on rational; 1580 1581 1582 1583psi(x+m) - psi(x+m-1) = 1/(x+m-1); 1584 1585 1586 1 1 1587-----------=----------- 1588 m + x - 1 m + x - 1 1589 1590psi(x+2) - psi(x+1) + 2*psi(x) = 1/(x+1) + 2*psi(x); 1591 1592 1593 2*psi(x)*x + 2*psi(x) + 1 2*psi(x)*x + 2*psi(x) + 1 1594---------------------------=--------------------------- 1595 x + 1 x + 1 1596 1597psi(x+2) + 3*psi(x) = 4*psi(x) + 1/x + 1/(x+1); 1598 1599 1600 2 2 1601 4*psi(x)*x + 4*psi(x)*x + 2*x + 1 4*psi(x)*x + 4*psi(x)*x + 2*x + 1 1602------------------------------------=------------------------------------ 1603 2 2 1604 x + x x + x 1605 1606 1607psi(x + 1) = psi(x) + 1/x; 1608 1609 1610 psi(x)*x + 1 psi(x)*x + 1 1611--------------=-------------- 1612 x x 1613 1614psi(x + 3/2) = psi(x + 1/2) + 1/(x + 1/2); 1615 1616 1617 1 1 1 1 1 1 1618 psi(x + ---)*x + ---*psi(x + ---) + 1 psi(x + ---)*x + ---*psi(x + ---) + 1 1619 2 2 2 2 2 2 1620---------------------------------------=--------------------------------------- 1621 1 1 1622 x + --- x + --- 1623 2 2 1624 1625psi(x - 1/2) = psi(x + 1/2) - 1/(x - 1/2); 1626 1627 1628 1 1 1 1 1 1 1629 psi(x + ---)*x - ---*psi(x + ---) - 1 psi(x + ---)*x - ---*psi(x + ---) - 1 1630 2 2 2 2 2 2 1631---------------------------------------=--------------------------------------- 1632 1 1 1633 x - --- x - --- 1634 2 2 1635 1636psi((x + 3a)/a); 1637 1638 1639 1 2 2 8 1640 psi(---*x)*x*(x + 6*x + 8) + 6*(x + 4*x + ---) 1641 2 3 1642-------------------------------------------------- 1643 2 1644 x*(x + 6*x + 8) 1645 psi(x/y + 3); 1646 1647 1648 x 2 2 2 2 2 1649 psi(---)*x*(x + 3*x*y + 2*y ) + 3*y*(x + 2*x*y + ---*y ) 1650 y 3 1651------------------------------------------------------------ 1652 2 2 1653 x*(x + 3*x*y + 2*y ) 1654 1655 1656off rational; 1657 1658 1659 1660% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 1661 1662% 6. Polygamma functions 1663 1664% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 1665 1666 1667procedure do!*one!*pg(n,x); 1668 write ("Polygamma (", n, ") of ", x, " is ", polygamma(n,x)); 1669 1670 1671do*one*pg 1672 1673 1674off rounded; 1675 1676 1677 1678do!*one!*pg(1,1/2); 1679 1680 1681 1 1 1682Polygamma (1) of --- is polygamma(1,---) 1683 2 2 1684 1685do!*one!*pg(1,1); 1686 1687 1688 2 1689 pi 1690Polygamma (1) of 1 is ----- 1691 6 1692 1693do!*one!*pg(1,3/2); 1694 1695 1696 2 1697 3 pi - 8 1698Polygamma (1) of --- is --------- 1699 2 2 1700 1701do!*one!*pg(1,1.005); 1702 1703 1704 201 201 1705Polygamma (1) of ----- is polygamma(1,-----) 1706 200 200 1707 1708do!*one!*pg(1,1.995); 1709 1710 1711 399 399 1712Polygamma (1) of ----- is polygamma(1,-----) 1713 200 200 1714 1715do!*one!*pg(1,1e-10); 1716 1717 1718 1 1 1719Polygamma (1) of ------------- is polygamma(1,-------------) 1720 10000000000 10000000000 1721 1722do!*one!*pg(2,1.45); 1723 1724 1725 29 29 1726Polygamma (2) of ---- is polygamma(2,----) 1727 20 20 1728 1729do!*one!*pg(3,1.99); 1730 1731 1732 199 199 1733Polygamma (3) of ----- is polygamma(3,-----) 1734 100 100 1735 1736do!*one!*pg(4,-8.2); 1737 1738 1739 - 41 - 41 1740Polygamma (4) of ------- is polygamma(4,-------) 1741 5 5 1742 1743do!*one!*pg(5,0); 1744 1745 1746 1747***** Polygamma undefined for nonpositive integer argument 0 1748 1749do!*one!*pg(6,-5); 1750 1751 1752 1753***** Polygamma undefined for nonpositive integer argument -5 1754 1755do!*one!*pg(7,200); 1756 1757 1758Polygamma (7) of 200 is (17726903568079021516229662669344581999513453462651624\ 1759 712682433450930396569413638060869523209196416456149981841411350319061723276\ 1760 968944831274405326841106087088051862580482604049179034792880997036306450715\ 1761 491134920388121743532178874504889199026667348488846246287054278592284199023\ 1762 548572837863642592371308428279823642858774260678182876022899303888558378920\ 1763 013392172441409952343098219076353830605697314645020537255667718925997023946\ 1764 826863459069360054494011515187931095594830347819766125471751832158677864778\ 1765 297413490571816668099535649328289203181141151677544880676008798702466775519\ 1766 536091686976761627732998715124407667063278175501392084867643186474774933465\ 1767 8 1768 396962161891279302009565617687762042880000000000000000000000*pi - 16820227\ 1769 432460991991188660317955383248583163197077694391321472430675801147397894113\ 1770 241309474829652161707416711766105349898340694530697667469860241947942732920\ 1771 236500114448913470876512035623237448423938602084906142995199152247445505854\ 1772 809437866123469569241946248640222536901257402027830808909074139755120553020\ 1773 556624279638002199727273508802505439369471450464398635245844612858514905584\ 1774 191236791869017030402868269742260341406479951357060228410068248515181595142\ 1775 787674466216948716753957289698597496283251496652438121703517099395342367021\ 1776 250291313681953557646793694608947926057983579614775135882107369446401248554\ 1777 435651401852361884349691269283596626501141334161214962487130496595028983095\ 1778 5139972163546512706990894178649281)/332379441901481653429306175050210912490\ 1779877252424717963362795627204944935676505713641303560172432808552812159526462818\ 1780482407311443167715586395099878270739132900972423384048825922106902366518694430\ 1781745950915458779757277282691228353896966672481750012784165867117882267723605328\ 1782731691535740709943298606962033030246693303602017387715928925429361947910469604\ 1783750251103233276436606433091607681634323856824649594135073543769729862444199003\ 1784003689857550501021762715909773708042403069021620614852595346852975209964593076\ 1785502948221562526866293424905422559646396593953966512675164975671252040991301719\ 1786130814280519993725908582643757436465790651101591268309746402030002476193040535\ 178746148691267935533164553830400000000000000000000000 1788 1789 1790on rounded; 1791 1792 1793precision 100; 1794 1795 1796139 1797 1798 1799do!*one!*pg(1,1/2); 1800 1801 1802Polygamma (1) of 0.5 is 1803 18044.9348022005446793094172454999380755676568497036203953132066746881100224112096\ 180502621500886701859276116 1806 1807do!*one!*pg(1,1); 1808 1809 1810Polygamma (1) of 1 is 1811 18121.6449340668482264364724151666460251892189499012067984377355582293700074704032\ 181300873833628900619758705 1814 1815do!*one!*pg(1,3/2); 1816 1817 1818Polygamma (1) of 1.5 is 1819 18200.9348022005446793094172454999380755676568497036203953132066746881100224112096\ 1821026215008867018592761159 1822 1823do!*one!*pg(1,1.005); 1824 1825 1826Polygamma (1) of 1.005 is 1827 18281.6329941567556809752535869786110269899606654266292810174237683064726679207401\ 182936690588658095268582677 1830 1831do!*one!*pg(1,1.995); 1832 1833 1834Polygamma (1) of 1.995 is 1835 18360.6469608286405823512476399271078276952436864784225077824256922477813603546774\ 1837633500406650324443323374 1838 1839do!*one!*pg(1,1e-10); 1840 1841 1842Polygamma (1) of 0.0000000001 is 1843 18441.0000000000000000000164493406660781505587296600657326399164207520577564247801\ 184580942170336642993019363e+20 1846 1847do!*one!*pg(2,1.45); 1848 1849 1850Polygamma (2) of 1.45 is - 1851 18520.9038374030762576882323095385298671928600903081114466582453675225591714826271\ 185366928803699348863802546 1854 1855do!*one!*pg(3,1.99); 1856 1857 1858Polygamma (3) of 1.99 is 1859 18600.5029071324168653201805109908625701971861516895613080444480934082942919777908\ 1861933506993776280887706183 1862 1863do!*one!*pg(4,-8.2); 1864 1865 1866Polygamma (4) of - 8.2 is 1867 186874935.512595774270527120292307813135522959054934662779176176297186107113915939\ 186937121099755096024434196 1870 1871do!*one!*pg(5,0); 1872 1873 1874 1875***** Polygamma undefined for nonpositive integer argument 0 1876 1877do!*one!*pg(6,-5); 1878 1879 1880 1881***** Polygamma undefined for nonpositive integer argument -5 1882 1883do!*one!*pg(7,200); 1884 1885 1886Polygamma (7) of 200 is 1887 18885.7240937253925583738370296815447272453468073681959561547435678473859266441297\ 188953317064645661270233713e-14 1890 1891 1892off rounded; 1893 1894 1895clear x; 1896 1897 1898 1899 1900% Polygamma differentiation has already 1901% been tried a bit in the psi section 1902 1903df(int(int(int(polygamma(3,x),x),x),x),x); 1904 1905 1906polygamma(1,x) 1907 1908 1909clear w, y, z; 1910 1911 1912 1913 1914 1915% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 1916 1917% 7. Zeta function 1918 1919% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 1920 1921 1922procedure do!*one!*zeta(n); 1923 write ("Zeta of ", n, " is ", zeta n); 1924 1925 1926do*one*zeta 1927 1928 1929off rounded; 1930 1931 1932clear x, y, z; 1933 1934 1935 1936z := x * ((x+y)**5 + (x**y)); 1937 1938 1939 y 5 4 3 2 2 3 4 5 1940z := x*(x + x + 5*x *y + 10*x *y + 10*x *y + 5*x*y + y ) 1941 1942 1943do!*one!*zeta(0); 1944 1945 1946 - 1 1947Zeta of 0 is ------ 1948 2 1949 1950 1951for k := 4 step 2 until 35 do 1952 do!*one!*zeta(k); 1953 1954 1955 4 1956 pi 1957Zeta of 4 is ----- 1958 90 1959 1960 6 1961 pi 1962Zeta of 6 is ----- 1963 945 1964 1965 8 1966 pi 1967Zeta of 8 is ------ 1968 9450 1969 1970 10 1971 pi 1972Zeta of 10 is ------- 1973 93555 1974 1975 12 1976 691*pi 1977Zeta of 12 is ----------- 1978 638512875 1979 1980 14 1981 2*pi 1982Zeta of 14 is ---------- 1983 18243225 1984 1985 16 1986 3617*pi 1987Zeta of 16 is -------------- 1988 325641566250 1989 1990 18 1991 43867*pi 1992Zeta of 18 is ---------------- 1993 38979295480125 1994 1995 20 1996 174611*pi 1997Zeta of 20 is ------------------ 1998 1531329465290625 1999 2000 22 2001 155366*pi 2002Zeta of 22 is ------------------- 2003 13447856940643125 2004 2005 24 2006 236364091*pi 2007Zeta of 24 is ----------------------- 2008 201919571963756521875 2009 2010 26 2011 1315862*pi 2012Zeta of 26 is ---------------------- 2013 11094481976030578125 2014 2015 28 2016 6785560294*pi 2017Zeta of 28 is -------------------------- 2018 564653660170076273671875 2019 2020 30 2021 6892673020804*pi 2022Zeta of 30 is ------------------------------ 2023 5660878804669082674070015625 2024 2025Zeta of 32 is zeta(32) 2026 2027Zeta of 34 is zeta(34) 2028 2029 2030for k := 1 step 2 until 31 do 2031 do!*one!*zeta(-k); 2032 2033 2034 - 1 2035Zeta of -1 is ------ 2036 12 2037 2038 1 2039Zeta of -3 is ----- 2040 120 2041 2042 - 1 2043Zeta of -5 is ------ 2044 252 2045 2046 1 2047Zeta of -7 is ----- 2048 240 2049 2050 - 1 2051Zeta of -9 is ------ 2052 132 2053 2054 691 2055Zeta of -11 is ------- 2056 32760 2057 2058 - 1 2059Zeta of -13 is ------ 2060 12 2061 2062 3617 2063Zeta of -15 is ------ 2064 8160 2065 2066 - 43867 2067Zeta of -17 is ---------- 2068 14364 2069 2070 174611 2071Zeta of -19 is -------- 2072 6600 2073 2074 - 77683 2075Zeta of -21 is ---------- 2076 276 2077 2078 236364091 2079Zeta of -23 is ----------- 2080 65520 2081 2082 - 657931 2083Zeta of -25 is ----------- 2084 12 2085 2086 3392780147 2087Zeta of -27 is ------------ 2088 3480 2089 2090 - 1723168255201 2091Zeta of -29 is ------------------ 2092 85932 2093 2094Zeta of -31 is zeta(-31) 2095 2096 2097do!*one!*zeta(-17/3); 2098 2099 2100 - 17 - 17 2101Zeta of ------- is zeta(-------) 2102 3 3 2103 2104do!*one!*zeta(190); 2105 2106 2107Zeta of 190 is zeta(190) 2108 2109do!*one!*zeta(300); 2110 2111 2112Zeta of 300 is zeta(300) 2113 2114do!*one!*zeta(0); 2115 2116 2117 - 1 2118Zeta of 0 is ------ 2119 2 2120 2121do!*one!*zeta(-44); 2122 2123 2124Zeta of -44 is 0 2125 2126 2127on rounded; 2128 2129 2130clear x, y; 2131 2132 2133 2134for k := 3 step 3 until 36 do << 2135 precision (31+k*3); 2136 do!*one!*zeta(k) >>; 2137 2138 2139Zeta of 3 is 1.202056903159594285399738161511449990765 2140 2141Zeta of 6 is 1.017343061984449139714517929790920527901817490033 2142 2143Zeta of 9 is 1.002008392826082214417852769232412060485605851394888756549 2144 2145Zeta of 12 is 2146 2147 1.00024608655330804829863799804773967096041608845800340453304095\ 2148 2133 2149 2150Zeta of 15 is 2151 2152 1.00003058823630702049355172851064506258762794870685817750656993\ 2153 2893332267156 2154 2155Zeta of 18 is 2156 2157 1.00000381729326499983985646164462193973045469721895333114317442\ 2158 9987630039542650045638 2159 2160Zeta of 21 is 2161 2162 1.00000047693298678780646311671960437304596644669478493760020748\ 2163 7376596839087898159833876638564 2164 2165Zeta of 24 is 2166 2167 1.00000005960818905125947961244020793580122750391883730279586424\ 2168 6972321724495355468544848206832825003614 2169 2170Zeta of 27 is 2171 2172 1.00000000745071178983542949198100417060411945471903188256582999\ 2173 3239578352147606271570867900837100313523764933952 2174 2175Zeta of 30 is 2176 2177 1.00000000093132743241966818287176473502121981356795513681618500\ 2178 8613360441960672940496363503624604027929086312123388047291 2179 2180Zeta of 33 is 2181 2182 1.00000000011641550172700519775929738354563095165224717276359325\ 2183 6517739947029124624567548673934974376008810870912845774213829513\ 2184 369 2185 2186Zeta of 36 is 2187 2188 1.00000000001455192189104198423592963224531842098380889412403806\ 2189 9139542218571745865030220152998942329578185363084791339999779092\ 2190 891491916899 2191 2192 2193precision 20; 2194 2195 2196139 2197 2198 2199do!*one!*zeta(-17/3); 2200 2201 2202Zeta of - 5.6666666666666666667 is - 0.0018766468228592287697 2203 2204do!*one!*zeta(z); 2205 2206 2207 y 5 4 3 2 2 3 4 5 2208Zeta of x*(x + x + 5*x *y + 10*x *y + 10*x *y + 5*x*y + y ) is zeta( 2209 2210 y 6 5 4 2 3 3 2 4 5 2211 x *x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + x*y ) 2212 2213 2214y := 3; 2215 2216 2217y := 3 2218 2219x := pi; 2220 2221 2222x := 3.1415926535897932385 2223 2224 2225do!*one!*zeta(z); 2226 2227 2228Zeta of 27548.203250393209469 is 1 2229 2230do!*one!*zeta(190); 2231 2232 2233Zeta of 190 is 1.0 2234 2235do!*one!*zeta(300); 2236 2237 2238Zeta of 300 is 1 2239 2240do!*one!*zeta(0); 2241 2242 2243Zeta of 0 is - 0.5 2244 2245do!*one!*zeta(-44); 2246 2247 2248Zeta of -44 is 0 2249 2250 2251off rounded; 2252 2253 2254 2255 2256 2257% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 2258 2259% 8. Kummer functions 2260 2261% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 2262 2263 2264off rounded; 2265 2266 2267 2268t!*kummer!*a := { 1, 2.4, -1397/10 }$ 2269 2270 2271t!*kummer!*b := { 0, 1, pi, -pi, 26 }$ 2272 2273 2274 2275for each a in t!*kummer!*a do 2276 for each b in t!*kummer!*a do 2277 for each z in t!*kummer!*a do 2278 << write "KummerM(", a, ",", b, ",", z, ") = ", 2279 KummerM(a,b,z); 2280 write "KummerU(", a, ",", b, ",", z, ") = ", 2281 KummerU(a,b,z) >>; 2282 2283 2284KummerM(1,1,1) = e 2285 2286KummerU(1,1,1) = kummeru(1,1,1) 2287 2288 12 2/5 2 2289KummerM(1,1,----) = e *e 2290 5 2291 2292 12 12 2293KummerU(1,1,----) = kummeru(1,1,----) 2294 5 5 2295 2296 - 1397 1 2297KummerM(1,1,---------) = ------------ 2298 10 7/10 139 2299 e *e 2300 2301 - 1397 - 1397 2302KummerU(1,1,---------) = kummeru(1,1,---------) 2303 10 10 2304 2305 12 12 2306KummerM(1,----,1) = kummerm(1,----,1) 2307 5 5 2308 2309 2 12 12 2310 2*gamma(---)*(gamma(----)*e - kummerm(1,----,1)) 2311 12 5 5 5 2312KummerU(1,----,1) = -------------------------------------------------- 2313 5 12 2314 5*gamma(----) 2315 5 2316 2317 12 12 12 12 2318KummerM(1,----,----) = kummerm(1,----,----) 2319 5 5 5 5 2320 2321 12 12 2322KummerU(1,----,----) = 2323 5 5 2324 2325 2 2/5 2/5 12 2 4/5 2/5 12 12 2326 gamma(---)*(5*e *5 *gamma(----)*e - 12*2 *3 *kummerm(1,----,----)) 2327 5 5 5 5 2328----------------------------------------------------------------------------- 2329 4/5 2/5 12 2330 30*2 *3 *gamma(----) 2331 5 2332 2333 12 - 1397 12 - 1397 2334KummerM(1,----,---------) = kummerm(1,----,---------) 2335 5 10 5 10 2336 2337 12 - 1397 2 2338KummerU(1,----,---------) = (2*gamma(---)*( 2339 5 10 5 2340 2341 7/10 2/5 12 - 1397 139 2342 - 1397*e *1397 *kummerm(1,----,---------)*e 2343 5 10 2344 2345 2/5 12 7/10 2/5 12 139 2346 - 10*10 *gamma(----)))/(6985*e *1397 *gamma(----)*e ) 2347 5 5 2348 2349 - 1397 - 1397 2350KummerM(1,---------,1) = kummerm(1,---------,1) 2351 10 10 2352 2353 - 1397 2354KummerU(1,---------,1) = 2355 10 2356 2357 1397 - 1397 3*pi 2358 1397*gamma(------)*kummerm(1,---------,1)*sin(------) - 10*e*pi 2359 10 10 10 2360----------------------------------------------------------------- 2361 1417 3*pi 2362 10*gamma(------)*sin(------) 2363 10 10 2364 2365 - 1397 12 - 1397 12 2366KummerM(1,---------,----) = kummerm(1,---------,----) 2367 10 5 10 5 2368 2369 - 1397 12 2370KummerU(1,---------,----) = ( - 4868940170769807140163734629614870951763530546\ 2371 10 5 2372 631554678436906268603895538747067202821442117249242625797089485978560806001\ 2373 2/5 2/5 7/10 2 2374 0798787187515790195560655355904*e *2 *3 *e *pi + 2004596689573651914\ 2375 834381033324557143448090555188728353940095378016295057932438794523477554321\ 2376 7/10 1397 - 1397 12 3*pi 2377 2890625*5 *gamma(------)*kummerm(1,---------,----)*sin(------))/(1434929\ 2378 10 10 5 10 2379 627468612680625899093288874118430988228481552150279237922703146068670321255\ 2380 7/10 1417 3*pi 2381 92231750488281250*5 *gamma(------)*sin(------)) 2382 10 10 2383 2384 - 1397 - 1397 - 1397 - 1397 2385KummerM(1,---------,---------) = kummerm(1,---------,---------) 2386 10 10 10 10 2387 2388 - 1397 - 1397 2389KummerU(1,---------,---------) = (1397*( - 15215998257931517360033101903862815\ 2390 10 10 2391 223888543388957222106115555299202666279048867916168002482075600873075777\ 2392 814303704269392393284644411305647344643215427879407971076364582034085385\ 2393 160268928702508481521778353248095651747223572373118125240197785695254459\ 2394 776199438476999663624567921028135476855359579600382069871166959862260275\ 2395 271370315144729355759279591209107609434598035344309681771044690476129730\ 2396 7/10 2397 6235868715700448137787799653833690839289133*( - 1397) *pi + 100000000\ 2398 000000000000000000000000000000000000000000000000000000000000000000000000\ 2399 7/10 7/10 2400 00000000000000000000000000000000000000000000000000000000000*e *10 2401 2402 1397 - 1397 - 1397 3*pi 139 2403 *gamma(------)*kummerm(1,---------,---------)*sin(------)*e ))/(100000\ 2404 10 10 10 10 2405 000000000000000000000000000000000000000000000000000000000000000000000000000\ 2406 7/10 7/10 2407 000000000000000000000000000000000000000000000000000000000000*e *10 2408 2409 1417 3*pi 139 2410 *gamma(------)*sin(------)*e ) 2411 10 10 2412 2413 12 12 2414KummerM(----,1,1) = kummerm(----,1,1) 2415 5 5 2416 2417 12 12 2418KummerU(----,1,1) = kummeru(----,1,1) 2419 5 5 2420 2421 12 12 12 12 2422KummerM(----,1,----) = kummerm(----,1,----) 2423 5 5 5 5 2424 2425 12 12 12 12 2426KummerU(----,1,----) = kummeru(----,1,----) 2427 5 5 5 5 2428 2429 12 - 1397 12 - 1397 2430KummerM(----,1,---------) = kummerm(----,1,---------) 2431 5 10 5 10 2432 2433 12 - 1397 12 - 1397 2434KummerU(----,1,---------) = kummeru(----,1,---------) 2435 5 10 5 10 2436 2437 12 12 2438KummerM(----,----,1) = e 2439 5 5 2440 2441 2 - 2 2*pi 2442 2*gamma(---)*kummerm(1,------,1)*sin(------) + 5*e*pi 2443 12 12 5 5 5 2444KummerU(----,----,1) = ------------------------------------------------------- 2445 5 5 12 2*pi 2446 5*gamma(----)*sin(------) 2447 5 5 2448 2449 12 12 12 2/5 2 2450KummerM(----,----,----) = e *e 2451 5 5 5 2452 2453 12 12 12 2454KummerU(----,----,----) = 2455 5 5 5 2456 2457 2/5 4/5 2/5 2 2/5 2 - 2 12 2*pi 2458 6*e *2 *3 *e *pi + 5 *gamma(---)*kummerm(1,------,----)*sin(------) 2459 5 5 5 5 2460----------------------------------------------------------------------------- 2461 4/5 2/5 12 2*pi 2462 6*2 *3 *gamma(----)*sin(------) 2463 5 5 2464 2465 12 12 - 1397 1 2466KummerM(----,----,---------) = ------------ 2467 5 5 10 7/10 139 2468 e *e 2469 2470 12 12 - 1397 2471KummerU(----,----,---------) = ( 2472 5 5 10 2473 2474 7/10 2/5 2 - 2 - 1397 2*pi 139 2475 - 4*e *10 *gamma(---)*kummerm(1,------,---------)*sin(------)*e 2476 5 5 10 5 2477 2478 2/5 7/10 2/5 12 2*pi 139 2479 + 1397*1397 *pi)/(1397*e *1397 *gamma(----)*sin(------)*e ) 2480 5 5 2481 2482 12 - 1397 12 - 1397 2483KummerM(----,---------,1) = kummerm(----,---------,1) 2484 5 10 5 10 2485 2486 12 - 1397 1431 1431 1417 2487KummerU(----,---------,1) = ( - 10*gamma(------)*kummerm(------,------,1)*pi + 2488 5 10 10 10 10 2489 2490 1417 1397 12 12 - 1397 2491 1397*gamma(------)*gamma(------)*gamma(----)*kummerm(----,---------,1) 2492 10 10 5 5 10 2493 2494 3*pi 1431 1417 12 3*pi 2495 *sin(------))/(10*gamma(------)*gamma(------)*gamma(----)*sin(------)) 2496 10 10 10 5 10 2497 2498 12 - 1397 12 12 - 1397 12 2499KummerM(----,---------,----) = kummerm(----,---------,----) 2500 5 10 5 5 10 5 2501 2502 12 - 1397 12 2503KummerU(----,---------,----) = (2004596689573651914834381033324557143448090555\ 2504 5 10 5 2505 7/10 1417 2506 1887283539400953780162950579324387945234775543212890625*5 *gamma(------) 2507 10 2508 2509 1397 12 12 - 1397 12 3*pi 2510 *gamma(------)*gamma(----)*kummerm(----,---------,----)*sin(------) - 48689\ 2511 10 5 5 10 5 10 2512 401707698071401637346296148709517635305466315546784369062686038955387470672\ 2513 2/5 2514 028214421172492426257970894859785608060010798787187515790195560655355904*2 2515 2516 7/10 1431 1431 1417 12 2517 *3 *gamma(------)*kummerm(------,------,----)*pi)/(143492962746861268062\ 2518 10 10 10 5 2519 589909328887411843098822848155215027923792270314606867032125592231750488281\ 2520 7/10 1431 1417 12 3*pi 2521 250*5 *gamma(------)*gamma(------)*gamma(----)*sin(------)) 2522 10 10 5 10 2523 2524 12 - 1397 - 1397 12 - 1397 - 1397 2525KummerM(----,---------,---------) = kummerm(----,---------,---------) 2526 5 10 10 5 10 10 2527 2528 12 - 1397 - 1397 2529KummerU(----,---------,---------) = (1397*( - 15215998257931517360033101903862\ 2530 5 10 10 2531 815223888543388957222106115555299202666279048867916168002482075600873075\ 2532 777814303704269392393284644411305647344643215427879407971076364582034085\ 2533 385160268928702508481521778353248095651747223572373118125240197785695254\ 2534 459776199438476999663624567921028135476855359579600382069871166959862260\ 2535 275271370315144729355759279591209107609434598035344309681771044690476129\ 2536 7/10 1431 2537 7306235868715700448137787799653833690839289133*( - 1397) *gamma(------) 2538 10 2539 2540 1431 1417 - 1397 2541 *kummerm(------,------,---------)*pi + 100000000000000000000000000000000\ 2542 10 10 10 2543 000000000000000000000000000000000000000000000000000000000000000000000000\ 2544 7/10 1417 1397 2545 00000000000000000000000000000000000*10 *gamma(------)*gamma(------) 2546 10 10 2547 2548 12 12 - 1397 - 1397 3*pi 2549 *gamma(----)*kummerm(----,---------,---------)*sin(------)))/(1000000000\ 2550 5 5 10 10 10 2551 000000000000000000000000000000000000000000000000000000000000000000000000000\ 2552 7/10 1431 2553 00000000000000000000000000000000000000000000000000000000*10 *gamma(------) 2554 10 2555 2556 1417 12 3*pi 2557 *gamma(------)*gamma(----)*sin(------)) 2558 10 5 10 2559 2560 - 1397 - 1397 2561KummerM(---------,1,1) = kummerm(---------,1,1) 2562 10 10 2563 2564 - 1397 - 1397 2565KummerU(---------,1,1) = kummeru(---------,1,1) 2566 10 10 2567 2568 - 1397 12 - 1397 12 2569KummerM(---------,1,----) = kummerm(---------,1,----) 2570 10 5 10 5 2571 2572 - 1397 12 - 1397 12 2573KummerU(---------,1,----) = kummeru(---------,1,----) 2574 10 5 10 5 2575 2576 - 1397 - 1397 - 1397 - 1397 2577KummerM(---------,1,---------) = kummerm(---------,1,---------) 2578 10 10 10 10 2579 2580 - 1397 - 1397 - 1397 - 1397 2581KummerU(---------,1,---------) = kummeru(---------,1,---------) 2582 10 10 10 10 2583 2584 - 1397 12 - 1397 12 2585KummerM(---------,----,1) = kummerm(---------,----,1) 2586 10 5 10 5 2587 2588 - 1397 12 2589KummerU(---------,----,1) = ( 2590 10 5 2591 2592 1411 - 1397 12 pi 2593 7055*gamma(------)*kummerm(---------,----,1)*sin(----)*pi + 2794 2594 10 10 5 10 2595 2596 1397 12 2 - 1411 - 2 3*pi 2597 *gamma(------)*gamma(----)*gamma(---)*kummerm(---------,------,1)*sin(------) 2598 10 5 5 10 5 10 2599 2600 2*pi 12 2*pi 2601 *sin(------))/(50*gamma(----)*sin(------)*pi) 2602 5 5 5 2603 2604 - 1397 12 12 - 1397 12 12 2605KummerM(---------,----,----) = kummerm(---------,----,----) 2606 10 5 5 10 5 5 2607 2608 - 1397 12 12 2/5 1397 12 2 2609KummerU(---------,----,----) = (1397*5 *gamma(------)*gamma(----)*gamma(---) 2610 10 5 5 10 5 5 2611 2612 - 1411 - 2 12 3*pi 2*pi 2613 *kummerm(---------,------,----)*sin(------)*sin(------) 2614 10 5 5 10 5 2615 2616 4/5 2/5 1411 - 1397 12 12 pi 2617 + 8466*2 *3 *gamma(------)*kummerm(---------,----,----)*sin(----)*pi)/( 2618 10 10 5 5 10 2619 2620 4/5 2/5 12 2*pi 2621 60*2 *3 *gamma(----)*sin(------)*pi) 2622 5 5 2623 2624 - 1397 12 - 1397 - 1397 12 - 1397 2625KummerM(---------,----,---------) = kummerm(---------,----,---------) 2626 10 5 10 10 5 10 2627 2628 - 1397 12 - 1397 2629KummerU(---------,----,---------) = ( 2630 10 5 10 2631 2632 2/5 1411 - 1397 12 - 1397 pi 2633 1411*1397 *gamma(------)*kummerm(---------,----,---------)*sin(----)*pi - 4 2634 10 10 5 10 10 2635 2636 2/5 1397 12 2 2637 *10 *gamma(------)*gamma(----)*gamma(---) 2638 10 5 5 2639 2640 - 1411 - 2 - 1397 3*pi 2*pi 2/5 2641 *kummerm(---------,------,---------)*sin(------)*sin(------))/(10*1397 2642 10 5 10 10 5 2643 2644 12 2*pi 2645 *gamma(----)*sin(------)*pi) 2646 5 5 2647 2648 - 1397 - 1397 2649KummerM(---------,---------,1) = e 2650 10 10 2651 2652 - 1397 - 1397 2653KummerU(---------,---------,1) = 2654 10 10 2655 2656 1397 1417 1417 2657 1397*gamma(------)*(gamma(------)*e - kummerm(1,------,1)) 2658 10 10 10 2659------------------------------------------------------------ 2660 1417 2661 10*gamma(------) 2662 10 2663 2664 - 1397 - 1397 12 2/5 2 2665KummerM(---------,---------,----) = e *e 2666 10 10 5 2667 2668 - 1397 - 1397 12 1397 2669KummerU(---------,---------,----) = (1397*gamma(------)*(717464813734306340312\ 2670 10 10 5 10 2671 949546644437059215494114240776075139618961351573034335160627961158752441\ 2672 2/5 7/10 1417 2 2673 40625*e *5 *gamma(------)*e - 243447008538490357008186731480743547\ 2674 10 2675 588176527331577733921845313430194776937353360141072105862462131289854474\ 2676 2/5 7/10 2677 29892804030005399393593757895097780327677952*2 *3 2678 2679 1417 12 2680 *kummerm(1,------,----)))/(717464813734306340312949546644437059215494114\ 2681 10 5 2682 7/10 1417 2683 240776075139618961351573034335160627961158752441406250*5 *gamma(------)) 2684 10 2685 2686 - 1397 - 1397 - 1397 1 2687KummerM(---------,---------,---------) = ------------ 2688 10 10 10 7/10 139 2689 e *e 2690 2691 - 1397 - 1397 - 1397 1397 2692KummerU(---------,---------,---------) = (1397*gamma(------)*( - 2125674956633\ 2693 10 10 10 10 2694 032975196624335969635286777229511437323928224343075298612479183126847888\ 2695 669946745961441968686160658227486434117341864824259398934046657195274753\ 2696 293559368132110161728306889569339740434868592435948758962549087133060524\ 2697 602096055630661627048030735061555236853008352138567630526116693733270173\ 2698 375161002024292757760455410433025718690999571358891912333038013345537600\ 2699 7/10 2700 06254341494325951532336811508595833526048489556116405666102486918801*e 2701 2702 7/10 1417 - 1397 139 2703 *( - 1397) *kummerm(1,------,---------)*e + 1000000000000000000000\ 2704 10 10 2705 000000000000000000000000000000000000000000000000000000000000000000000000\ 2706 7/10 1417 2707 00000000000000000000000000000000000000000000000*10 *gamma(------)))/( 2708 10 2709 100000000000000000000000000000000000000000000000000000000000000000000000000\ 2710 7/10 2711 0000000000000000000000000000000000000000000000000000000000000000000*e 2712 2713 7/10 1417 139 2714 *10 *gamma(------)*e ) 2715 10 2716 2717 2718on rounded; 2719 2720 2721precision 30; 2722 2723 272420 2725 2726t!*k!*c := 7; 2727 2728 2729t*k*c := 7 2730 2731 2732% To test each and every possible combination of 2733% three arguments from t!*kummer!*b would take too 2734% long, but we want the possibility of trying most 2735% special cases. Compromise: test every seventh 2736% possibility. 2737 2738for each a in t!*kummer!*b do 2739 for each b in t!*kummer!*b do 2740 for each z in t!*kummer!*b do 2741 << if t!*k!*c = 7 2742 then << write "KummerM(", a, ",", b, ",", z, ") = ", 2743 KummerM(a,b,z); 2744 write "KummerU(", a, ",", b, ",", z, ") = ", 2745 KummerU(a,b,z); 2746 t!*k!*c := 0 >>; 2747 t!*k!*c := t!*k!*c + 1 >>; 2748 2749 2750KummerM(0,0,0) = kummerm(0,0,0) 2751 2752KummerU(0,0,0) = kummeru(0,0,0) 2753 2754KummerM(0,1,3.14159265358979323846264338328) = 1 2755 2756KummerU(0,1,3.14159265358979323846264338328) = kummeru(0,1, 2757 2758 3.14159265358979323846264338328) 2759 2760KummerM(0,3.14159265358979323846264338328,26) = 1 2761 2762KummerU(0,3.14159265358979323846264338328,26) = kummeru(0, 2763 2764 3.14159265358979323846264338328,26) 2765 2766KummerM(0,26,1) = 1 2767 2768KummerU(0,26,1) = kummeru(0,26,1) 2769 2770KummerM(1,0, - 3.14159265358979323846264338328) = kummerm(1,0, 2771 2772 - 3.14159265358979323846264338328) 2773 2774KummerU(1,0, - 3.14159265358979323846264338328) = kummeru(1,0, 2775 2776 - 3.14159265358979323846264338328) 2777 2778KummerM(1,3.14159265358979323846264338328,0) = 1 2779 2780KummerU(1,3.14159265358979323846264338328,0) = kummeru(1, 2781 2782 3.14159265358979323846264338328,0) 2783 2784KummerM(1, - 3.14159265358979323846264338328,3.14159265358979323846264338328) = 2785 27862692.89480079631357528203659153 2787 2788KummerU(1, - 3.14159265358979323846264338328,3.14159265358979323846264338328) = 2789 27900.129554194296952806409644905659 2791 2792KummerM(1,26,26) = 7.74565667206271943920803547594 2793 2794KummerU(1,26,26) = kummeru(1,26,26) 2795 2796KummerM(3.14159265358979323846264338328,1,1) = 10.2259987795328570162092950355 2797 2798KummerU(3.14159265358979323846264338328,1,1) = kummeru( 2799 2800 3.14159265358979323846264338328,1,1) 2801 2802KummerM(3.14159265358979323846264338328,3.14159265358979323846264338328, 2803 2804 - 3.14159265358979323846264338328) = 0.0432139182637722497744177371717 2805 2806KummerU(3.14159265358979323846264338328,3.14159265358979323846264338328, 2807 2808 - 3.14159265358979323846264338328) = ( - 0.137891580772667438638357954721 2809 2810 2.14159265358979323846264338328 2811 *( - 3.14159265358979323846264338328) 2812 2813 + 1.22938452238615186004844111454)/ 2814 2815 2.14159265358979323846264338328 2816( - 3.14159265358979323846264338328) 2817 2818KummerM(3.14159265358979323846264338328,26,0) = 1 2819 2820KummerU(3.14159265358979323846264338328,26,0) = kummeru( 2821 2822 3.14159265358979323846264338328,26,0) 2823 2824KummerM( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328) = 2825 2826kummerm( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328) 2827 2828KummerU( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328) = 2829 2830kummeru( - 3.14159265358979323846264338328,0,3.14159265358979323846264338328) 2831 2832KummerM( - 3.14159265358979323846264338328,1,26) = 2833 28346.18522226564722800173513559462e+5 2835 2836KummerU( - 3.14159265358979323846264338328,1,26) = kummeru( 2837 2838 - 3.14159265358979323846264338328,1,26) 2839 2840KummerM( - 3.14159265358979323846264338328, - 3.14159265358979323846264338328,1 2841 2842) = 2.71828182845904523536028747135 2843 2844KummerU( - 3.14159265358979323846264338328, - 3.14159265358979323846264338328,1 2845 2846) = 19.2419564406028465661346237348 2847 2848KummerM( - 3.14159265358979323846264338328,26, - 3.14159265358979323846264338328 2849 2850) = 1.42892253084220157246185820464 2851 2852KummerU( - 3.14159265358979323846264338328,26, - 3.14159265358979323846264338328 2853 2854) = kummeru( - 3.14159265358979323846264338328,26, 2855 2856 - 3.14159265358979323846264338328) 2857 2858KummerM(26,1,0) = 1 2859 2860KummerU(26,1,0) = kummeru(26,1,0) 2861 2862KummerM(26,3.14159265358979323846264338328,3.14159265358979323846264338328) = 2863 28643.91638029828702661403357541917e+5 2865 2866KummerU(26,3.14159265358979323846264338328,3.14159265358979323846264338328) = 2867 28684.18995913372628050180833640475e-32 2869 2870KummerM(26, - 3.14159265358979323846264338328,26) = 2871 28722.19471945265322419268333614674e+34 2873 2874KummerU(26, - 3.14159265358979323846264338328,26) = 0 2875 2876 2877off rounded; 2878 2879 2880clear x, y, z, t!*k!*c; 2881 2882 2883 2884df(df(KummerM(a,b,z),z),z); 2885 2886 2887 2 2888(kummerm(2,3,z)*z - 2*kummerm(2,3,z)*z + 2*kummerm(2,3,z) + 2*kummerm(1,3,z)*z 2889 2890 2 2891 - 4*kummerm(1,3,z) + 2*kummerm(0,3,z))/z 2892 2893df(KummerU(a,b,z),z); 2894 2895 2896 kummeru(2,3,z)*z - kummeru(2,3,z) - kummeru(1,3,z) 2897---------------------------------------------------- 2898 z 2899 2900 2901z := ((x^2 + y)^5) + (x^(x+y)); 2902 2903 2904 x + y 10 8 6 2 4 3 2 4 5 2905z := x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y 2906 2907 2908df(df(KummerM(a,b,z),y),x); 2909 2910 2911 4*x + 4*y 2912(x 2913 2914 x + y 10 8 6 2 4 3 2 4 5 2915 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2916 2917 2 4*x + 4*y 2918 *log(x) *x + x 2919 2920 x + y 10 8 6 2 4 3 2 4 5 2921 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 2922 2923 4*x + 4*y 2924 *x + x 2925 2926 x + y 10 8 6 2 4 3 2 4 5 2927 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 2928 2929 3*x + 3*y 2930 *y + 2*x 2931 2932 x + y 10 8 6 2 4 3 2 4 5 2933 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2934 2935 2 11 3*x + 3*y 2936 *log(x) *x + 10*x 2937 2938 x + y 10 8 6 2 4 3 2 4 5 2939 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2940 2941 2 9 3*x + 3*y 2942 *log(x) *x *y + 20*x 2943 2944 x + y 10 8 6 2 4 3 2 4 5 2945 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2946 2947 2 7 2 3*x + 3*y 2948 *log(x) *x *y + 20*x 2949 2950 x + y 10 8 6 2 4 3 2 4 5 2951 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2952 2953 2 5 3 3*x + 3*y 2954 *log(x) *x *y + 10*x 2955 2956 x + y 10 8 6 2 4 3 2 4 5 2957 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2958 2959 2 3 4 3*x + 3*y 2960 *log(x) *x *y + 2*x 2961 2962 x + y 10 8 6 2 4 3 2 4 5 2963 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2964 2965 2 5 3*x + 3*y 2966 *log(x) *x*y - x 2967 2968 x + y 10 8 6 2 4 3 2 4 5 2969 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 2970 2971 2 3*x + 3*y 2972 *log(x) *x + 2*x 2973 2974 x + y 10 8 6 2 4 3 2 4 5 2975 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 2976 2977 11 3*x + 3*y 2978 *x + 2*x 2979 2980 x + y 10 8 6 2 4 3 2 4 5 2981 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 2982 2983 10 3*x + 3*y 2984 *x *y + 10*x 2985 2986 x + y 10 8 6 2 4 3 2 4 5 2987 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 2988 2989 10 3*x + 3*y 2990 *x + 10*x 2991 2992 x + y 10 8 6 2 4 3 2 4 5 2993 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 2994 2995 9 3*x + 3*y 2996 *x *y + 5*x 2997 2998 x + y 10 8 6 2 4 3 2 4 5 2999 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3000 3001 9 3*x + 3*y 3002 *x + 10*x 3003 3004 x + y 10 8 6 2 4 3 2 4 5 3005 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3006 3007 8 2 3*x + 3*y 3008 *x *y + 40*x 3009 3010 x + y 10 8 6 2 4 3 2 4 5 3011 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3012 3013 8 3*x + 3*y 3014 *x *y + 20*x 3015 3016 x + y 10 8 6 2 4 3 2 4 5 3017 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3018 3019 7 2 3*x + 3*y 3020 *x *y + 20*x 3021 3022 x + y 10 8 6 2 4 3 2 4 5 3023 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3024 3025 7 3*x + 3*y 3026 *x *y + 20*x 3027 3028 x + y 10 8 6 2 4 3 2 4 5 3029 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3030 3031 6 3 3*x + 3*y 3032 *x *y + 60*x 3033 3034 x + y 10 8 6 2 4 3 2 4 5 3035 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3036 3037 6 2 3*x + 3*y 3038 *x *y + 20*x 3039 3040 x + y 10 8 6 2 4 3 2 4 5 3041 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3042 3043 5 3 3*x + 3*y 3044 *x *y + 30*x 3045 3046 x + y 10 8 6 2 4 3 2 4 5 3047 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3048 3049 5 2 3*x + 3*y 3050 *x *y + 20*x 3051 3052 x + y 10 8 6 2 4 3 2 4 5 3053 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3054 3055 4 4 3*x + 3*y 3056 *x *y + 40*x 3057 3058 x + y 10 8 6 2 4 3 2 4 5 3059 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3060 3061 4 3 3*x + 3*y 3062 *x *y + 10*x 3063 3064 x + y 10 8 6 2 4 3 2 4 5 3065 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3066 3067 3 4 3*x + 3*y 3068 *x *y + 20*x 3069 3070 x + y 10 8 6 2 4 3 2 4 5 3071 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3072 3073 3 3 3*x + 3*y 3074 *x *y + 10*x 3075 3076 x + y 10 8 6 2 4 3 2 4 5 3077 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3078 3079 2 5 3*x + 3*y 3080 *x *y + 10*x 3081 3082 x + y 10 8 6 2 4 3 2 4 5 3083 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3084 3085 2 4 3*x + 3*y 3086 *x *y + 2*x 3087 3088 x + y 10 8 6 2 4 3 2 4 5 3089 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3090 3091 5 3*x + 3*y 3092 *x*y + 5*x 3093 3094 x + y 10 8 6 2 4 3 2 4 5 3095 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3096 3097 4 3*x + 3*y 3098 *x*y - x 3099 3100 x + y 10 8 6 2 4 3 2 4 5 3101 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3102 3103 3*x + 3*y 3104 *x + 2*x 3105 3106 x + y 10 8 6 2 4 3 2 4 5 3107 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3108 3109 6 3*x + 3*y 3110 *y - x 3111 3112 x + y 10 8 6 2 4 3 2 4 5 3113 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3114 3115 3*x + 3*y 3116 *y + 5*x 3117 3118 x + y 10 8 6 2 4 3 2 4 5 9 3119 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5 3120 3121 3*x + 3*y 3122 *x 3123 3124 x + y 10 8 6 2 4 3 2 4 5 8 3125 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 3126 3127 3*x + 3*y 3128 20*x 3129 3130 x + y 10 8 6 2 4 3 2 4 5 7 3131 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 3132 3133 3*x + 3*y 3134 20*x 3135 3136 x + y 10 8 6 2 4 3 2 4 5 6 2 3137 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3138 3139 3*x + 3*y 3140 + 30*x 3141 3142 x + y 10 8 6 2 4 3 2 4 5 5 2 3143 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3144 3145 3*x + 3*y 3146 + 30*x 3147 3148 x + y 10 8 6 2 4 3 2 4 5 4 3 3149 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3150 3151 3*x + 3*y 3152 + 20*x 3153 3154 x + y 10 8 6 2 4 3 2 4 5 3 3 3155 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3156 3157 3*x + 3*y 3158 + 20*x 3159 3160 x + y 10 8 6 2 4 3 2 4 5 2 4 3161 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3162 3163 3*x + 3*y 3164 + 5*x 3165 3166 x + y 10 8 6 2 4 3 2 4 5 4 3167 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 3168 3169 3*x + 3*y 3170 5*x 3171 3172 x + y 10 8 6 2 4 3 2 4 5 5 3173 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 3174 3175 3*x + 3*y 3176 x 3177 3178 x + y 10 8 6 2 4 3 2 4 5 3179 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) + 2 3180 3181 3*x + 3*y 3182 *x 3183 3184 x + y 10 8 6 2 4 3 2 4 5 3185 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3186 3187 2 3*x + 3*y 3188 *log(x) *x + 2*x 3189 3190 x + y 10 8 6 2 4 3 2 4 5 3191 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3192 3193 3*x + 3*y 3194 *x + 2*x 3195 3196 x + y 10 8 6 2 4 3 2 4 5 3197 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3198 3199 2*x + 2*y 3200 *y + x 3201 3202 x + y 10 8 6 2 4 3 2 4 5 3203 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3204 3205 2 21 2*x + 2*y 3206 *log(x) *x + 10*x 3207 3208 x + y 10 8 6 2 4 3 2 4 5 3209 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3210 3211 2 19 2*x + 2*y 3212 *log(x) *x *y + 45*x 3213 3214 x + y 10 8 6 2 4 3 2 4 5 3215 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3216 3217 2 17 2 2*x + 2*y 3218 *log(x) *x *y + 120*x 3219 3220 x + y 10 8 6 2 4 3 2 4 5 3221 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3222 3223 2 15 3 2*x + 2*y 3224 *log(x) *x *y + 210*x 3225 3226 x + y 10 8 6 2 4 3 2 4 5 3227 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3228 3229 2 13 4 2*x + 2*y 3230 *log(x) *x *y + 252*x 3231 3232 x + y 10 8 6 2 4 3 2 4 5 3233 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3234 3235 2 11 5 2*x + 2*y 3236 *log(x) *x *y + 210*x 3237 3238 x + y 10 8 6 2 4 3 2 4 5 3239 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3240 3241 2 9 6 2*x + 2*y 3242 *log(x) *x *y + 120*x 3243 3244 x + y 10 8 6 2 4 3 2 4 5 3245 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3246 3247 2 7 7 2*x + 2*y 3248 *log(x) *x *y + 45*x 3249 3250 x + y 10 8 6 2 4 3 2 4 5 3251 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3252 3253 2 5 8 2*x + 2*y 3254 *log(x) *x *y + 10*x 3255 3256 x + y 10 8 6 2 4 3 2 4 5 3257 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3258 3259 2 3 9 2*x + 2*y 3260 *log(x) *x *y + x 3261 3262 x + y 10 8 6 2 4 3 2 4 5 3263 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3264 3265 2 10 2*x + 2*y 3266 *log(x) *x*y + x 3267 3268 x + y 10 8 6 2 4 3 2 4 5 3269 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3270 3271 2 2*x + 2*y 3272 *log(x) *x + x 3273 3274 x + y 10 8 6 2 4 3 2 4 5 3275 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3276 3277 21 2*x + 2*y 3278 *x + x 3279 3280 x + y 10 8 6 2 4 3 2 4 5 3281 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3282 3283 20 2*x + 2*y 3284 *x *y + 20*x 3285 3286 x + y 10 8 6 2 4 3 2 4 5 3287 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3288 3289 20 2*x + 2*y 3290 *x + 10*x 3291 3292 x + y 10 8 6 2 4 3 2 4 5 3293 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3294 3295 19 2*x + 2*y 3296 *x *y + 10*x 3297 3298 x + y 10 8 6 2 4 3 2 4 5 3299 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3300 3301 19 2*x + 2*y 3302 *x + 10*x 3303 3304 x + y 10 8 6 2 4 3 2 4 5 3305 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3306 3307 18 2 2*x + 2*y 3308 *x *y + 180*x 3309 3310 x + y 10 8 6 2 4 3 2 4 5 3311 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3312 3313 18 2*x + 2*y 3314 *x *y + 45*x 3315 3316 x + y 10 8 6 2 4 3 2 4 5 3317 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3318 3319 17 2 2*x + 2*y 3320 *x *y + 90*x 3321 3322 x + y 10 8 6 2 4 3 2 4 5 3323 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3324 3325 17 2*x + 2*y 3326 *x *y + 45*x 3327 3328 x + y 10 8 6 2 4 3 2 4 5 3329 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3330 3331 16 3 2*x + 2*y 3332 *x *y + 720*x 3333 3334 x + y 10 8 6 2 4 3 2 4 5 3335 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3336 3337 16 2 2*x + 2*y 3338 *x *y + 120*x 3339 3340 x + y 10 8 6 2 4 3 2 4 5 3341 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3342 3343 15 3 2*x + 2*y 3344 *x *y + 360*x 3345 3346 x + y 10 8 6 2 4 3 2 4 5 3347 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3348 3349 15 2 2*x + 2*y 3350 *x *y + 120*x 3351 3352 x + y 10 8 6 2 4 3 2 4 5 3353 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3354 3355 14 4 2*x + 2*y 3356 *x *y + 1680*x 3357 3358 x + y 10 8 6 2 4 3 2 4 5 3359 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3360 3361 14 3 2*x + 2*y 3362 *x *y + 210*x 3363 3364 x + y 10 8 6 2 4 3 2 4 5 3365 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3366 3367 13 4 2*x + 2*y 3368 *x *y + 840*x 3369 3370 x + y 10 8 6 2 4 3 2 4 5 3371 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3372 3373 13 3 2*x + 2*y 3374 *x *y + 210*x 3375 3376 x + y 10 8 6 2 4 3 2 4 5 3377 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3378 3379 12 5 2*x + 2*y 3380 *x *y + 2520*x 3381 3382 x + y 10 8 6 2 4 3 2 4 5 3383 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3384 3385 12 4 2*x + 2*y 3386 *x *y + 252*x 3387 3388 x + y 10 8 6 2 4 3 2 4 5 3389 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3390 3391 11 5 2*x + 2*y 3392 *x *y + 1260*x 3393 3394 x + y 10 8 6 2 4 3 2 4 5 3395 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3396 3397 11 4 2*x + 2*y 3398 *x *y + 252*x 3399 3400 x + y 10 8 6 2 4 3 2 4 5 3401 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3402 3403 10 6 2*x + 2*y 3404 *x *y + 2520*x 3405 3406 x + y 10 8 6 2 4 3 2 4 5 3407 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3408 3409 10 5 2*x + 2*y 3410 *x *y - 20*x 3411 3412 x + y 10 8 6 2 4 3 2 4 5 3413 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3414 3415 10 2*x + 2*y 3416 *x + 210*x 3417 3418 x + y 10 8 6 2 4 3 2 4 5 3419 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3420 3421 9 6 2*x + 2*y 3422 *x *y + 1260*x 3423 3424 x + y 10 8 6 2 4 3 2 4 5 3425 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3426 3427 9 5 2*x + 2*y 3428 *x *y - 10*x 3429 3430 x + y 10 8 6 2 4 3 2 4 5 3431 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3432 3433 9 2*x + 2*y 3434 *x + 210*x 3435 3436 x + y 10 8 6 2 4 3 2 4 5 3437 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3438 3439 8 7 2*x + 2*y 3440 *x *y + 1680*x 3441 3442 x + y 10 8 6 2 4 3 2 4 5 3443 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3444 3445 8 6 2*x + 2*y 3446 *x *y - 80*x 3447 3448 x + y 10 8 6 2 4 3 2 4 5 3449 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3450 3451 8 2*x + 2*y 3452 *x *y + 120*x 3453 3454 x + y 10 8 6 2 4 3 2 4 5 3455 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3456 3457 7 7 2*x + 2*y 3458 *x *y + 840*x 3459 3460 x + y 10 8 6 2 4 3 2 4 5 3461 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3462 3463 7 6 2*x + 2*y 3464 *x *y - 40*x 3465 3466 x + y 10 8 6 2 4 3 2 4 5 3467 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3468 3469 7 2*x + 2*y 3470 *x *y + 120*x 3471 3472 x + y 10 8 6 2 4 3 2 4 5 3473 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3474 3475 6 8 2*x + 2*y 3476 *x *y + 720*x 3477 3478 x + y 10 8 6 2 4 3 2 4 5 3479 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3480 3481 6 7 2*x + 2*y 3482 *x *y - 120*x 3483 3484 x + y 10 8 6 2 4 3 2 4 5 3485 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3486 3487 6 2 2*x + 2*y 3488 *x *y + 45*x 3489 3490 x + y 10 8 6 2 4 3 2 4 5 3491 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3492 3493 5 8 2*x + 2*y 3494 *x *y + 360*x 3495 3496 x + y 10 8 6 2 4 3 2 4 5 3497 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3498 3499 5 7 2*x + 2*y 3500 *x *y - 60*x 3501 3502 x + y 10 8 6 2 4 3 2 4 5 3503 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3504 3505 5 2 2*x + 2*y 3506 *x *y + 45*x 3507 3508 x + y 10 8 6 2 4 3 2 4 5 3509 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3510 3511 4 9 2*x + 2*y 3512 *x *y + 180*x 3513 3514 x + y 10 8 6 2 4 3 2 4 5 3515 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3516 3517 4 8 2*x + 2*y 3518 *x *y - 80*x 3519 3520 x + y 10 8 6 2 4 3 2 4 5 3521 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3522 3523 4 3 2*x + 2*y 3524 *x *y + 10*x 3525 3526 x + y 10 8 6 2 4 3 2 4 5 3527 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3528 3529 3 9 2*x + 2*y 3530 *x *y + 90*x 3531 3532 x + y 10 8 6 2 4 3 2 4 5 3533 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3534 3535 3 8 2*x + 2*y 3536 *x *y - 40*x 3537 3538 x + y 10 8 6 2 4 3 2 4 5 3539 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3540 3541 3 3 2*x + 2*y 3542 *x *y + 10*x 3543 3544 x + y 10 8 6 2 4 3 2 4 5 3545 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3546 3547 2 10 2*x + 2*y 3548 *x *y + 20*x 3549 3550 x + y 10 8 6 2 4 3 2 4 5 3551 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3552 3553 2 9 2*x + 2*y 3554 *x *y - 20*x 3555 3556 x + y 10 8 6 2 4 3 2 4 5 3557 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3558 3559 2 4 2*x + 2*y 3560 *x *y + x 3561 3562 x + y 10 8 6 2 4 3 2 4 5 3563 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3564 3565 10 2*x + 2*y 3566 *x*y + 10*x 3567 3568 x + y 10 8 6 2 4 3 2 4 5 3569 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3570 3571 9 2*x + 2*y 3572 *x*y - 10*x 3573 3574 x + y 10 8 6 2 4 3 2 4 5 3575 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3576 3577 4 2*x + 2*y 3578 *x*y + x 3579 3580 x + y 10 8 6 2 4 3 2 4 5 3581 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3582 3583 2*x + 2*y 3584 *x + x 3585 3586 x + y 10 8 6 2 4 3 2 4 5 3587 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3588 3589 11 2*x + 2*y 3590 *y + x 3591 3592 x + y 10 8 6 2 4 3 2 4 5 3593 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3594 3595 2*x + 2*y 3596 *y + 10*x 3597 3598 x + y 10 8 6 2 4 3 2 4 5 19 3599 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 3600 3601 2*x + 2*y 3602 10*x 3603 3604 x + y 10 8 6 2 4 3 2 4 5 18 3605 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3606 3607 2*x + 2*y 3608 + 50*x 3609 3610 x + y 10 8 6 2 4 3 2 4 5 18 3611 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 3612 3613 2*x + 2*y 3614 90*x 3615 3616 x + y 10 8 6 2 4 3 2 4 5 17 3617 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3618 3619 2*x + 2*y 3620 + 90*x 3621 3622 x + y 10 8 6 2 4 3 2 4 5 16 2 3623 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3624 3625 2*x + 2*y 3626 + 400*x 3627 3628 x + y 10 8 6 2 4 3 2 4 5 16 3629 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3630 3631 2*x + 2*y 3632 + 360*x 3633 3634 x + y 10 8 6 2 4 3 2 4 5 15 2 3635 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3636 3637 2*x + 2*y 3638 + 360*x 3639 3640 x + y 10 8 6 2 4 3 2 4 5 14 3 3641 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3642 3643 2*x + 2*y 3644 + 1400*x 3645 3646 x + y 10 8 6 2 4 3 2 4 5 14 2 3647 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3648 3649 2*x + 2*y 3650 + 840*x 3651 3652 x + y 10 8 6 2 4 3 2 4 5 13 3 3653 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3654 3655 2*x + 2*y 3656 + 840*x 3657 3658 x + y 10 8 6 2 4 3 2 4 5 12 4 3659 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3660 3661 2*x + 2*y 3662 + 2800*x 3663 3664 x + y 10 8 6 2 4 3 2 4 5 12 3 3665 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3666 3667 2*x + 2*y 3668 + 1260*x 3669 3670 x + y 10 8 6 2 4 3 2 4 5 11 4 3671 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3672 3673 2*x + 2*y 3674 + 1260*x 3675 3676 x + y 10 8 6 2 4 3 2 4 5 10 5 3677 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3678 3679 2*x + 2*y 3680 + 3500*x 3681 3682 x + y 10 8 6 2 4 3 2 4 5 10 4 3683 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3684 3685 2*x + 2*y 3686 + 2*x 3687 3688 x + y 10 8 6 2 4 3 2 4 5 10 3689 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 3690 3691 2*x + 2*y 3692 1260*x 3693 3694 x + y 10 8 6 2 4 3 2 4 5 9 5 3695 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3696 3697 2*x + 2*y 3698 - 10*x 3699 3700 x + y 10 8 6 2 4 3 2 4 5 9 3701 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 3702 3703 2*x + 2*y 3704 1260*x 3705 3706 x + y 10 8 6 2 4 3 2 4 5 8 6 3707 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3708 3709 2*x + 2*y 3710 + 2800*x 3711 3712 x + y 10 8 6 2 4 3 2 4 5 8 5 3713 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3714 3715 2*x + 2*y 3716 + 40*x 3717 3718 x + y 10 8 6 2 4 3 2 4 5 8 3719 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 3720 3721 2*x + 2*y 3722 840*x 3723 3724 x + y 10 8 6 2 4 3 2 4 5 7 6 3725 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3726 3727 2*x + 2*y 3728 - 40*x 3729 3730 x + y 10 8 6 2 4 3 2 4 5 7 3731 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 3732 3733 2*x + 2*y 3734 840*x 3735 3736 x + y 10 8 6 2 4 3 2 4 5 6 7 3737 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3738 3739 2*x + 2*y 3740 + 1400*x 3741 3742 x + y 10 8 6 2 4 3 2 4 5 6 6 3743 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3744 3745 2*x + 2*y 3746 - 20*x 3747 3748 x + y 10 8 6 2 4 3 2 4 5 6 2 3749 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3750 3751 2*x + 2*y 3752 + 120*x 3753 3754 x + y 10 8 6 2 4 3 2 4 5 6 3755 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 3756 3757 2*x + 2*y 3758 360*x 3759 3760 x + y 10 8 6 2 4 3 2 4 5 5 7 3761 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3762 3763 2*x + 2*y 3764 - 60*x 3765 3766 x + y 10 8 6 2 4 3 2 4 5 5 2 3767 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3768 3769 2*x + 2*y 3770 + 360*x 3771 3772 x + y 10 8 6 2 4 3 2 4 5 4 8 3773 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3774 3775 2*x + 2*y 3776 + 400*x 3777 3778 x + y 10 8 6 2 4 3 2 4 5 4 7 3779 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3780 3781 2*x + 2*y 3782 - 40*x 3783 3784 x + y 10 8 6 2 4 3 2 4 5 4 3 3785 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3786 3787 2*x + 2*y 3788 + 120*x 3789 3790 x + y 10 8 6 2 4 3 2 4 5 4 2 3791 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3792 3793 2*x + 2*y 3794 + 90*x 3795 3796 x + y 10 8 6 2 4 3 2 4 5 3 8 3797 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3798 3799 2*x + 2*y 3800 - 40*x 3801 3802 x + y 10 8 6 2 4 3 2 4 5 3 3 3803 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3804 3805 2*x + 2*y 3806 + 90*x 3807 3808 x + y 10 8 6 2 4 3 2 4 5 2 9 3809 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3810 3811 2*x + 2*y 3812 + 50*x 3813 3814 x + y 10 8 6 2 4 3 2 4 5 2 8 3815 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3816 3817 2*x + 2*y 3818 - 30*x 3819 3820 x + y 10 8 6 2 4 3 2 4 5 2 4 3821 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3822 3823 2*x + 2*y 3824 + 40*x 3825 3826 x + y 10 8 6 2 4 3 2 4 5 2 3 3827 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 3828 3829 2*x + 2*y 3830 + 10*x 3831 3832 x + y 10 8 6 2 4 3 2 4 5 9 3833 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y - 3834 3835 2*x + 2*y 3836 10*x 3837 3838 x + y 10 8 6 2 4 3 2 4 5 4 3839 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 3840 3841 2*x + 2*y 3842 10*x 3843 3844 x + y 10 8 6 2 4 3 2 4 5 10 3845 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y - 3846 3847 2*x + 2*y 3848 8*x 3849 3850 x + y 10 8 6 2 4 3 2 4 5 5 3851 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y - 3852 3853 2*x + 2*y 3854 x 3855 3856 x + y 10 8 6 2 4 3 2 4 5 3857 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) + 2 3858 3859 2*x + 2*y 3860 *x 3861 3862 x + y 10 8 6 2 4 3 2 4 5 3863 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3864 3865 2 11 2*x + 2*y 3866 *log(x) *x + 10*x 3867 3868 x + y 10 8 6 2 4 3 2 4 5 3869 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3870 3871 2 9 2*x + 2*y 3872 *log(x) *x *y + 20*x 3873 3874 x + y 10 8 6 2 4 3 2 4 5 3875 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3876 3877 2 7 2 2*x + 2*y 3878 *log(x) *x *y + 20*x 3879 3880 x + y 10 8 6 2 4 3 2 4 5 3881 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3882 3883 2 5 3 2*x + 2*y 3884 *log(x) *x *y + 10*x 3885 3886 x + y 10 8 6 2 4 3 2 4 5 3887 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3888 3889 2 3 4 2*x + 2*y 3890 *log(x) *x *y + 2*x 3891 3892 x + y 10 8 6 2 4 3 2 4 5 3893 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3894 3895 2 5 2*x + 2*y 3896 *log(x) *x*y - 3*x 3897 3898 x + y 10 8 6 2 4 3 2 4 5 3899 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 3900 3901 2 2*x + 2*y 3902 *log(x) *x + 2*x 3903 3904 x + y 10 8 6 2 4 3 2 4 5 3905 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3906 3907 11 2*x + 2*y 3908 *x + 2*x 3909 3910 x + y 10 8 6 2 4 3 2 4 5 3911 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3912 3913 10 2*x + 2*y 3914 *x *y + 20*x 3915 3916 x + y 10 8 6 2 4 3 2 4 5 3917 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3918 3919 10 2*x + 2*y 3920 *x + 10*x 3921 3922 x + y 10 8 6 2 4 3 2 4 5 3923 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3924 3925 9 2*x + 2*y 3926 *x *y + 10*x 3927 3928 x + y 10 8 6 2 4 3 2 4 5 3929 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3930 3931 9 2*x + 2*y 3932 *x + 10*x 3933 3934 x + y 10 8 6 2 4 3 2 4 5 3935 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3936 3937 8 2 2*x + 2*y 3938 *x *y + 80*x 3939 3940 x + y 10 8 6 2 4 3 2 4 5 3941 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3942 3943 8 2*x + 2*y 3944 *x *y + 20*x 3945 3946 x + y 10 8 6 2 4 3 2 4 5 3947 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3948 3949 7 2 2*x + 2*y 3950 *x *y + 40*x 3951 3952 x + y 10 8 6 2 4 3 2 4 5 3953 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3954 3955 7 2*x + 2*y 3956 *x *y + 20*x 3957 3958 x + y 10 8 6 2 4 3 2 4 5 3959 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3960 3961 6 3 2*x + 2*y 3962 *x *y + 120*x 3963 3964 x + y 10 8 6 2 4 3 2 4 5 3965 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3966 3967 6 2 2*x + 2*y 3968 *x *y + 20*x 3969 3970 x + y 10 8 6 2 4 3 2 4 5 3971 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3972 3973 5 3 2*x + 2*y 3974 *x *y + 60*x 3975 3976 x + y 10 8 6 2 4 3 2 4 5 3977 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3978 3979 5 2 2*x + 2*y 3980 *x *y + 20*x 3981 3982 x + y 10 8 6 2 4 3 2 4 5 3983 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3984 3985 4 4 2*x + 2*y 3986 *x *y + 80*x 3987 3988 x + y 10 8 6 2 4 3 2 4 5 3989 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3990 3991 4 3 2*x + 2*y 3992 *x *y + 10*x 3993 3994 x + y 10 8 6 2 4 3 2 4 5 3995 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 3996 3997 3 4 2*x + 2*y 3998 *x *y + 40*x 3999 4000 x + y 10 8 6 2 4 3 2 4 5 4001 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4002 4003 3 3 2*x + 2*y 4004 *x *y + 10*x 4005 4006 x + y 10 8 6 2 4 3 2 4 5 4007 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4008 4009 2 5 2*x + 2*y 4010 *x *y + 20*x 4011 4012 x + y 10 8 6 2 4 3 2 4 5 4013 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4014 4015 2 4 2*x + 2*y 4016 *x *y + 2*x 4017 4018 x + y 10 8 6 2 4 3 2 4 5 4019 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4020 4021 5 2*x + 2*y 4022 *x*y + 10*x 4023 4024 x + y 10 8 6 2 4 3 2 4 5 4025 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4026 4027 4 2*x + 2*y 4028 *x*y - 3*x 4029 4030 x + y 10 8 6 2 4 3 2 4 5 4031 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4032 4033 2*x + 2*y 4034 *x + 2*x 4035 4036 x + y 10 8 6 2 4 3 2 4 5 4037 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4038 4039 6 2*x + 2*y 4040 *y - 3*x 4041 4042 x + y 10 8 6 2 4 3 2 4 5 4043 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4044 4045 2*x + 2*y 4046 *y + 10*x 4047 4048 x + y 10 8 6 2 4 3 2 4 5 9 4049 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 4050 4051 2*x + 2*y 4052 10*x 4053 4054 x + y 10 8 6 2 4 3 2 4 5 8 4055 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 4056 4057 2*x + 2*y 4058 40*x 4059 4060 x + y 10 8 6 2 4 3 2 4 5 7 4061 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 4062 4063 2*x + 2*y 4064 40*x 4065 4066 x + y 10 8 6 2 4 3 2 4 5 6 2 4067 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4068 4069 2*x + 2*y 4070 + 60*x 4071 4072 x + y 10 8 6 2 4 3 2 4 5 5 2 4073 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4074 4075 2*x + 2*y 4076 + 60*x 4077 4078 x + y 10 8 6 2 4 3 2 4 5 4 3 4079 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4080 4081 2*x + 2*y 4082 + 40*x 4083 4084 x + y 10 8 6 2 4 3 2 4 5 3 3 4085 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4086 4087 2*x + 2*y 4088 + 40*x 4089 4090 x + y 10 8 6 2 4 3 2 4 5 2 4 4091 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4092 4093 2*x + 2*y 4094 + 10*x 4095 4096 x + y 10 8 6 2 4 3 2 4 5 4 4097 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 4098 4099 2*x + 2*y 4100 10*x 4101 4102 x + y 10 8 6 2 4 3 2 4 5 5 4103 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 4104 4105 2*x + 2*y 4106 x 4107 4108 x + y 10 8 6 2 4 3 2 4 5 4109 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) + 2 4110 4111 2*x + 2*y 4112 *x 4113 4114 x + y 10 8 6 2 4 3 2 4 5 4115 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4116 4117 2 2*x + 2*y 4118 *log(x) *x + 2*x 4119 4120 x + y 10 8 6 2 4 3 2 4 5 4121 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4122 4123 2*x + 2*y 4124 *x + 2*x 4125 4126 x + y 10 8 6 2 4 3 2 4 5 4127 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4128 4129 x + y 4130 *y + x 4131 4132 x + y 10 8 6 2 4 3 2 4 5 4133 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4134 4135 2 21 x + y 4136 *log(x) *x + 10*x 4137 4138 x + y 10 8 6 2 4 3 2 4 5 4139 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4140 4141 2 19 x + y 4142 *log(x) *x *y + 45*x 4143 4144 x + y 10 8 6 2 4 3 2 4 5 4145 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4146 4147 2 17 2 x + y 4148 *log(x) *x *y + 120*x 4149 4150 x + y 10 8 6 2 4 3 2 4 5 4151 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4152 4153 2 15 3 x + y 4154 *log(x) *x *y + 210*x 4155 4156 x + y 10 8 6 2 4 3 2 4 5 4157 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4158 4159 2 13 4 x + y 4160 *log(x) *x *y + 252*x 4161 4162 x + y 10 8 6 2 4 3 2 4 5 4163 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4164 4165 2 11 5 x + y 4166 *log(x) *x *y - x 4167 4168 x + y 10 8 6 2 4 3 2 4 5 4169 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4170 4171 2 11 x + y 4172 *log(x) *x + 210*x 4173 4174 x + y 10 8 6 2 4 3 2 4 5 4175 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4176 4177 2 9 6 x + y 4178 *log(x) *x *y - 5*x 4179 4180 x + y 10 8 6 2 4 3 2 4 5 4181 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4182 4183 2 9 x + y 4184 *log(x) *x *y + 120*x 4185 4186 x + y 10 8 6 2 4 3 2 4 5 4187 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4188 4189 2 7 7 x + y 4190 *log(x) *x *y - 10*x 4191 4192 x + y 10 8 6 2 4 3 2 4 5 4193 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4194 4195 2 7 2 x + y 4196 *log(x) *x *y + 45*x 4197 4198 x + y 10 8 6 2 4 3 2 4 5 4199 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4200 4201 2 5 8 x + y 4202 *log(x) *x *y - 10*x 4203 4204 x + y 10 8 6 2 4 3 2 4 5 4205 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4206 4207 2 5 3 x + y 4208 *log(x) *x *y + 10*x 4209 4210 x + y 10 8 6 2 4 3 2 4 5 4211 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4212 4213 2 3 9 x + y 4214 *log(x) *x *y - 5*x 4215 4216 x + y 10 8 6 2 4 3 2 4 5 4217 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4218 4219 2 3 4 x + y 4220 *log(x) *x *y + x 4221 4222 x + y 10 8 6 2 4 3 2 4 5 4223 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4224 4225 2 10 x + y 4226 *log(x) *x*y - x 4227 4228 x + y 10 8 6 2 4 3 2 4 5 4229 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 4230 4231 2 5 x + y 4232 *log(x) *x*y + 10*x 4233 4234 x + y 10 8 6 2 4 3 2 4 5 4235 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4236 4237 30 x + y 4238 *x + 5*x 4239 4240 x + y 10 8 6 2 4 3 2 4 5 4241 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4242 4243 29 x + y 4244 *x + 140*x 4245 4246 x + y 10 8 6 2 4 3 2 4 5 4247 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4248 4249 28 x + y 4250 *x *y + 70*x 4251 4252 x + y 10 8 6 2 4 3 2 4 5 4253 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4254 4255 27 x + y 4256 *x *y + 910*x 4257 4258 x + y 10 8 6 2 4 3 2 4 5 4259 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4260 4261 26 2 x + y 4262 *x *y + 455*x 4263 4264 x + y 10 8 6 2 4 3 2 4 5 4265 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4266 4267 25 2 x + y 4268 *x *y + 3640*x 4269 4270 x + y 10 8 6 2 4 3 2 4 5 4271 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4272 4273 24 3 x + y 4274 *x *y + 1820*x 4275 4276 x + y 10 8 6 2 4 3 2 4 5 4277 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4278 4279 23 3 x + y 4280 *x *y + 10010*x 4281 4282 x + y 10 8 6 2 4 3 2 4 5 4283 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4284 4285 22 4 x + y 4286 *x *y + 5005*x 4287 4288 x + y 10 8 6 2 4 3 2 4 5 4289 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4290 4291 21 4 x + y 4292 *x *y + x 4293 4294 x + y 10 8 6 2 4 3 2 4 5 4295 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4296 4297 21 x + y 4298 *x + 20020*x 4299 4300 x + y 10 8 6 2 4 3 2 4 5 4301 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4302 4303 20 5 x + y 4304 *x *y + x 4305 4306 x + y 10 8 6 2 4 3 2 4 5 4307 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4308 4309 20 x + y 4310 *x *y - 20*x 4311 4312 x + y 10 8 6 2 4 3 2 4 5 4313 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4314 4315 20 x + y 4316 *x + 10010*x 4317 4318 x + y 10 8 6 2 4 3 2 4 5 4319 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4320 4321 19 5 x + y 4322 *x *y + 10*x 4323 4324 x + y 10 8 6 2 4 3 2 4 5 4325 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4326 4327 19 x + y 4328 *x *y - 10*x 4329 4330 x + y 10 8 6 2 4 3 2 4 5 4331 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4332 4333 19 x + y 4334 *x + 30030*x 4335 4336 x + y 10 8 6 2 4 3 2 4 5 4337 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4338 4339 18 6 x + y 4340 *x *y + 10*x 4341 4342 x + y 10 8 6 2 4 3 2 4 5 4343 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4344 4345 18 2 x + y 4346 *x *y - 180*x 4347 4348 x + y 10 8 6 2 4 3 2 4 5 4349 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4350 4351 18 x + y 4352 *x *y + 15015*x 4353 4354 x + y 10 8 6 2 4 3 2 4 5 4355 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4356 4357 17 6 x + y 4358 *x *y + 45*x 4359 4360 x + y 10 8 6 2 4 3 2 4 5 4361 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4362 4363 17 2 x + y 4364 *x *y - 90*x 4365 4366 x + y 10 8 6 2 4 3 2 4 5 4367 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4368 4369 17 x + y 4370 *x *y + 34320*x 4371 4372 x + y 10 8 6 2 4 3 2 4 5 4373 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4374 4375 16 7 x + y 4376 *x *y + 45*x 4377 4378 x + y 10 8 6 2 4 3 2 4 5 4379 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4380 4381 16 3 x + y 4382 *x *y - 720*x 4383 4384 x + y 10 8 6 2 4 3 2 4 5 4385 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4386 4387 16 2 x + y 4388 *x *y + 17160*x 4389 4390 x + y 10 8 6 2 4 3 2 4 5 4391 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4392 4393 15 7 x + y 4394 *x *y + 120*x 4395 4396 x + y 10 8 6 2 4 3 2 4 5 4397 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4398 4399 15 3 x + y 4400 *x *y - 360*x 4401 4402 x + y 10 8 6 2 4 3 2 4 5 4403 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4404 4405 15 2 x + y 4406 *x *y + 30030*x 4407 4408 x + y 10 8 6 2 4 3 2 4 5 4409 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4410 4411 14 8 x + y 4412 *x *y + 120*x 4413 4414 x + y 10 8 6 2 4 3 2 4 5 4415 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4416 4417 14 4 x + y 4418 *x *y - 1680*x 4419 4420 x + y 10 8 6 2 4 3 2 4 5 4421 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4422 4423 14 3 x + y 4424 *x *y + 15015*x 4425 4426 x + y 10 8 6 2 4 3 2 4 5 4427 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4428 4429 13 8 x + y 4430 *x *y + 210*x 4431 4432 x + y 10 8 6 2 4 3 2 4 5 4433 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4434 4435 13 4 x + y 4436 *x *y - 840*x 4437 4438 x + y 10 8 6 2 4 3 2 4 5 4439 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4440 4441 13 3 x + y 4442 *x *y + 20020*x 4443 4444 x + y 10 8 6 2 4 3 2 4 5 4445 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4446 4447 12 9 x + y 4448 *x *y + 210*x 4449 4450 x + y 10 8 6 2 4 3 2 4 5 4451 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4452 4453 12 5 x + y 4454 *x *y - 2520*x 4455 4456 x + y 10 8 6 2 4 3 2 4 5 4457 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4458 4459 12 4 x + y 4460 *x *y + 10010*x 4461 4462 x + y 10 8 6 2 4 3 2 4 5 4463 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4464 4465 11 9 x + y 4466 *x *y + 252*x 4467 4468 x + y 10 8 6 2 4 3 2 4 5 4469 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4470 4471 11 5 x + y 4472 *x *y - 1260*x 4473 4474 x + y 10 8 6 2 4 3 2 4 5 4475 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4476 4477 11 4 x + y 4478 *x *y - x 4479 4480 x + y 10 8 6 2 4 3 2 4 5 4481 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4482 4483 11 x + y 4484 *x + 10010*x 4485 4486 x + y 10 8 6 2 4 3 2 4 5 4487 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4488 4489 10 10 x + y 4490 *x *y + 252*x 4491 4492 x + y 10 8 6 2 4 3 2 4 5 4493 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4494 4495 10 6 x + y 4496 *x *y - 2520*x 4497 4498 x + y 10 8 6 2 4 3 2 4 5 4499 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4500 4501 10 5 x + y 4502 *x *y - x 4503 4504 x + y 10 8 6 2 4 3 2 4 5 4505 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4506 4507 10 x + y 4508 *x *y + 20*x 4509 4510 x + y 10 8 6 2 4 3 2 4 5 4511 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4512 4513 10 x + y 4514 *x + 5005*x 4515 4516 x + y 10 8 6 2 4 3 2 4 5 4517 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4518 4519 9 10 x + y 4520 *x *y + 210*x 4521 4522 x + y 10 8 6 2 4 3 2 4 5 4523 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4524 4525 9 6 x + y 4526 *x *y - 1260*x 4527 4528 x + y 10 8 6 2 4 3 2 4 5 4529 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4530 4531 9 5 x + y 4532 *x *y - 5*x 4533 4534 x + y 10 8 6 2 4 3 2 4 5 4535 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4536 4537 9 x + y 4538 *x *y + 10*x 4539 4540 x + y 10 8 6 2 4 3 2 4 5 4541 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4542 4543 9 x + y 4544 *x + 3640*x 4545 4546 x + y 10 8 6 2 4 3 2 4 5 4547 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4548 4549 8 11 x + y 4550 *x *y + 210*x 4551 4552 x + y 10 8 6 2 4 3 2 4 5 4553 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4554 4555 8 7 x + y 4556 *x *y - 1680*x 4557 4558 x + y 10 8 6 2 4 3 2 4 5 4559 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4560 4561 8 6 x + y 4562 *x *y - 5*x 4563 4564 x + y 10 8 6 2 4 3 2 4 5 4565 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4566 4567 8 2 x + y 4568 *x *y + 80*x 4569 4570 x + y 10 8 6 2 4 3 2 4 5 4571 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4572 4573 8 x + y 4574 *x *y + 1820*x 4575 4576 x + y 10 8 6 2 4 3 2 4 5 4577 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4578 4579 7 11 x + y 4580 *x *y + 120*x 4581 4582 x + y 10 8 6 2 4 3 2 4 5 4583 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4584 4585 7 7 x + y 4586 *x *y - 840*x 4587 4588 x + y 10 8 6 2 4 3 2 4 5 4589 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4590 4591 7 6 x + y 4592 *x *y - 10*x 4593 4594 x + y 10 8 6 2 4 3 2 4 5 4595 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4596 4597 7 2 x + y 4598 *x *y + 40*x 4599 4600 x + y 10 8 6 2 4 3 2 4 5 4601 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4602 4603 7 x + y 4604 *x *y + 910*x 4605 4606 x + y 10 8 6 2 4 3 2 4 5 4607 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4608 4609 6 12 x + y 4610 *x *y + 120*x 4611 4612 x + y 10 8 6 2 4 3 2 4 5 4613 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4614 4615 6 8 x + y 4616 *x *y - 720*x 4617 4618 x + y 10 8 6 2 4 3 2 4 5 4619 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4620 4621 6 7 x + y 4622 *x *y - 10*x 4623 4624 x + y 10 8 6 2 4 3 2 4 5 4625 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4626 4627 6 3 x + y 4628 *x *y + 120*x 4629 4630 x + y 10 8 6 2 4 3 2 4 5 4631 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4632 4633 6 2 x + y 4634 *x *y + 455*x 4635 4636 x + y 10 8 6 2 4 3 2 4 5 4637 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4638 4639 5 12 x + y 4640 *x *y + 45*x 4641 4642 x + y 10 8 6 2 4 3 2 4 5 4643 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4644 4645 5 8 x + y 4646 *x *y - 360*x 4647 4648 x + y 10 8 6 2 4 3 2 4 5 4649 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4650 4651 5 7 x + y 4652 *x *y - 10*x 4653 4654 x + y 10 8 6 2 4 3 2 4 5 4655 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4656 4657 5 3 x + y 4658 *x *y + 60*x 4659 4660 x + y 10 8 6 2 4 3 2 4 5 4661 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4662 4663 5 2 x + y 4664 *x *y + 140*x 4665 4666 x + y 10 8 6 2 4 3 2 4 5 4667 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4668 4669 4 13 x + y 4670 *x *y + 45*x 4671 4672 x + y 10 8 6 2 4 3 2 4 5 4673 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4674 4675 4 9 x + y 4676 *x *y - 180*x 4677 4678 x + y 10 8 6 2 4 3 2 4 5 4679 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4680 4681 4 8 x + y 4682 *x *y - 10*x 4683 4684 x + y 10 8 6 2 4 3 2 4 5 4685 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4686 4687 4 4 x + y 4688 *x *y + 80*x 4689 4690 x + y 10 8 6 2 4 3 2 4 5 4691 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4692 4693 4 3 x + y 4694 *x *y + 70*x 4695 4696 x + y 10 8 6 2 4 3 2 4 5 4697 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4698 4699 3 13 x + y 4700 *x *y + 10*x 4701 4702 x + y 10 8 6 2 4 3 2 4 5 4703 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4704 4705 3 9 x + y 4706 *x *y - 90*x 4707 4708 x + y 10 8 6 2 4 3 2 4 5 4709 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4710 4711 3 8 x + y 4712 *x *y - 5*x 4713 4714 x + y 10 8 6 2 4 3 2 4 5 4715 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4716 4717 3 4 x + y 4718 *x *y + 40*x 4719 4720 x + y 10 8 6 2 4 3 2 4 5 4721 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4722 4723 3 3 x + y 4724 *x *y + 10*x 4725 4726 x + y 10 8 6 2 4 3 2 4 5 4727 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4728 4729 2 14 x + y 4730 *x *y + 10*x 4731 4732 x + y 10 8 6 2 4 3 2 4 5 4733 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4734 4735 2 10 x + y 4736 *x *y - 20*x 4737 4738 x + y 10 8 6 2 4 3 2 4 5 4739 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4740 4741 2 9 x + y 4742 *x *y - 5*x 4743 4744 x + y 10 8 6 2 4 3 2 4 5 4745 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4746 4747 2 5 x + y 4748 *x *y + 20*x 4749 4750 x + y 10 8 6 2 4 3 2 4 5 4751 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4752 4753 2 4 x + y 4754 *x *y + 5*x 4755 4756 x + y 10 8 6 2 4 3 2 4 5 4757 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4758 4759 14 x + y 4760 *x*y + x 4761 4762 x + y 10 8 6 2 4 3 2 4 5 4763 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4764 4765 10 x + y 4766 *x*y - 10*x 4767 4768 x + y 10 8 6 2 4 3 2 4 5 4769 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4770 4771 9 x + y 4772 *x*y - x 4773 4774 x + y 10 8 6 2 4 3 2 4 5 4775 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4776 4777 5 x + y 4778 *x*y + 10*x 4779 4780 x + y 10 8 6 2 4 3 2 4 5 4781 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4782 4783 4 x + y 4784 *x*y + x 4785 4786 x + y 10 8 6 2 4 3 2 4 5 4787 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4788 4789 11 x + y 4790 *y - x 4791 4792 x + y 10 8 6 2 4 3 2 4 5 4793 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 4794 4795 6 x + y 4796 *y + 5*x 4797 4798 x + y 10 8 6 2 4 3 2 4 5 29 4799 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 4800 4801 x + y 4802 5*x 4803 4804 x + y 10 8 6 2 4 3 2 4 5 28 4805 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4806 4807 x + y 4808 + 100*x 4809 4810 x + y 10 8 6 2 4 3 2 4 5 28 4811 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 4812 4813 x + y 4814 70*x 4815 4816 x + y 10 8 6 2 4 3 2 4 5 27 4817 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4818 4819 x + y 4820 + 70*x 4821 4822 x + y 10 8 6 2 4 3 2 4 5 26 2 4823 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4824 4825 x + y 4826 + 1300*x 4827 4828 x + y 10 8 6 2 4 3 2 4 5 26 4829 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4830 4831 x + y 4832 + 455*x 4833 4834 x + y 10 8 6 2 4 3 2 4 5 25 2 4835 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4836 4837 x + y 4838 + 455*x 4839 4840 x + y 10 8 6 2 4 3 2 4 5 24 3 4841 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4842 4843 x + y 4844 + 7800*x 4845 4846 x + y 10 8 6 2 4 3 2 4 5 24 2 4847 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4848 4849 x + y 4850 + 1820*x 4851 4852 x + y 10 8 6 2 4 3 2 4 5 23 3 4853 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4854 4855 x + y 4856 + 1820*x 4857 4858 x + y 10 8 6 2 4 3 2 4 5 22 4 4859 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4860 4861 x + y 4862 + 28600*x 4863 4864 x + y 10 8 6 2 4 3 2 4 5 22 3 4865 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4866 4867 x + y 4868 + 5005*x 4869 4870 x + y 10 8 6 2 4 3 2 4 5 21 4 4871 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4872 4873 x + y 4874 + 5005*x 4875 4876 x + y 10 8 6 2 4 3 2 4 5 20 5 4877 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4878 4879 x + y 4880 + 71500*x 4881 4882 x + y 10 8 6 2 4 3 2 4 5 20 4 4883 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4884 4885 x + y 4886 + x 4887 4888 x + y 10 8 6 2 4 3 2 4 5 20 4889 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 4890 4891 x + y 4892 10010*x 4893 4894 x + y 10 8 6 2 4 3 2 4 5 19 5 4895 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4896 4897 x + y 4898 - 10*x 4899 4900 x + y 10 8 6 2 4 3 2 4 5 19 4901 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 4902 4903 x + y 4904 10010*x 4905 4906 x + y 10 8 6 2 4 3 2 4 5 18 6 4907 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4908 4909 x + y 4910 + 128700*x 4911 4912 x + y 10 8 6 2 4 3 2 4 5 18 5 4913 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4914 4915 x + y 4916 - 20*x 4917 4918 x + y 10 8 6 2 4 3 2 4 5 18 4919 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 4920 4921 x + y 4922 15015*x 4923 4924 x + y 10 8 6 2 4 3 2 4 5 17 6 4925 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4926 4927 x + y 4928 - 90*x 4929 4930 x + y 10 8 6 2 4 3 2 4 5 17 4931 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4932 4933 x + y 4934 + 15015*x 4935 4936 x + y 10 8 6 2 4 3 2 4 5 16 7 4937 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4938 4939 x + y 4940 + 171600*x 4941 4942 x + y 10 8 6 2 4 3 2 4 5 16 6 4943 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4944 4945 x + y 4946 - 45*x 4947 4948 x + y 10 8 6 2 4 3 2 4 5 16 2 4949 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4950 4951 x + y 4952 - 160*x 4953 4954 x + y 10 8 6 2 4 3 2 4 5 16 4955 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4956 4957 x + y 4958 + 17160*x 4959 4960 x + y 10 8 6 2 4 3 2 4 5 15 7 4961 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4962 4963 x + y 4964 - 360*x 4965 4966 x + y 10 8 6 2 4 3 2 4 5 15 2 4967 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4968 4969 x + y 4970 + 17160*x 4971 4972 x + y 10 8 6 2 4 3 2 4 5 14 8 4973 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4974 4975 x + y 4976 + 171600*x 4977 4978 x + y 10 8 6 2 4 3 2 4 5 14 7 4979 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4980 4981 x + y 4982 - 240*x 4983 4984 x + y 10 8 6 2 4 3 2 4 5 14 3 4985 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4986 4987 x + y 4988 - 560*x 4989 4990 x + y 10 8 6 2 4 3 2 4 5 14 2 4991 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4992 4993 x + y 4994 + 15015*x 4995 4996 x + y 10 8 6 2 4 3 2 4 5 13 8 4997 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 4998 4999 x + y 5000 - 840*x 5001 5002 x + y 10 8 6 2 4 3 2 4 5 13 3 5003 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5004 5005 x + y 5006 + 15015*x 5007 5008 x + y 10 8 6 2 4 3 2 4 5 12 9 5009 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5010 5011 x + y 5012 + 128700*x 5013 5014 x + y 10 8 6 2 4 3 2 4 5 12 8 5015 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5016 5017 x + y 5018 - 630*x 5019 5020 x + y 10 8 6 2 4 3 2 4 5 12 4 5021 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5022 5023 x + y 5024 - 1120*x 5025 5026 x + y 10 8 6 2 4 3 2 4 5 12 3 5027 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5028 5029 x + y 5030 + 10010*x 5031 5032 x + y 10 8 6 2 4 3 2 4 5 11 9 5033 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5034 5035 x + y 5036 - 1260*x 5037 5038 x + y 10 8 6 2 4 3 2 4 5 11 4 5039 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5040 5041 x + y 5042 + 10010*x 5043 5044 x + y 10 8 6 2 4 3 2 4 5 10 5045 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 5046 5047 10 x + y 5048 *y + 71500*x 5049 5050 x + y 10 8 6 2 4 3 2 4 5 10 9 5051 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5052 5053 x + y 5054 - 1008*x 5055 5056 x + y 10 8 6 2 4 3 2 4 5 10 5 5057 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5058 5059 x + y 5060 - 1400*x 5061 5062 x + y 10 8 6 2 4 3 2 4 5 10 4 5063 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5064 5065 x + y 5066 - x 5067 5068 x + y 10 8 6 2 4 3 2 4 5 10 5069 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5070 5071 x + y 5072 5005*x 5073 5074 x + y 10 8 6 2 4 3 2 4 5 9 10 5075 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5076 5077 x + y 5078 - 1260*x 5079 5080 x + y 10 8 6 2 4 3 2 4 5 9 5 5081 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5082 5083 x + y 5084 + 10*x 5085 5086 x + y 10 8 6 2 4 3 2 4 5 9 5087 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5088 5089 x + y 5090 5005*x 5091 5092 x + y 10 8 6 2 4 3 2 4 5 8 11 5093 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5094 5095 x + y 5096 + 28600*x 5097 5098 x + y 10 8 6 2 4 3 2 4 5 8 10 5099 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5100 5101 x + y 5102 - 1050*x 5103 5104 x + y 10 8 6 2 4 3 2 4 5 8 6 5105 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5106 5107 x + y 5108 - 1120*x 5109 5110 x + y 10 8 6 2 4 3 2 4 5 8 5 5111 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5112 5113 x + y 5114 + 5*x 5115 5116 x + y 10 8 6 2 4 3 2 4 5 8 5117 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y - 5118 5119 x + y 5120 40*x 5121 5122 x + y 10 8 6 2 4 3 2 4 5 8 5123 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5124 5125 x + y 5126 1820*x 5127 5128 x + y 10 8 6 2 4 3 2 4 5 7 11 5129 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5130 5131 x + y 5132 - 840*x 5133 5134 x + y 10 8 6 2 4 3 2 4 5 7 6 5135 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5136 5137 x + y 5138 + 40*x 5139 5140 x + y 10 8 6 2 4 3 2 4 5 7 5141 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5142 5143 x + y 5144 1820*x 5145 5146 x + y 10 8 6 2 4 3 2 4 5 6 12 5147 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5148 5149 x + y 5150 + 7800*x 5151 5152 x + y 10 8 6 2 4 3 2 4 5 6 11 5153 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5154 5155 x + y 5156 - 720*x 5157 5158 x + y 10 8 6 2 4 3 2 4 5 6 7 5159 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5160 5161 x + y 5162 - 560*x 5163 5164 x + y 10 8 6 2 4 3 2 4 5 6 6 5165 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5166 5167 x + y 5168 + 30*x 5169 5170 x + y 10 8 6 2 4 3 2 4 5 6 2 5171 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5172 5173 x + y 5174 - 120*x 5175 5176 x + y 10 8 6 2 4 3 2 4 5 6 5177 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5178 5179 x + y 5180 455*x 5181 5182 x + y 10 8 6 2 4 3 2 4 5 5 12 5183 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5184 5185 x + y 5186 - 360*x 5187 5188 x + y 10 8 6 2 4 3 2 4 5 5 7 5189 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5190 5191 x + y 5192 + 60*x 5193 5194 x + y 10 8 6 2 4 3 2 4 5 5 2 5195 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5196 5197 x + y 5198 + 455*x 5199 5200 x + y 10 8 6 2 4 3 2 4 5 4 13 5201 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5202 5203 x + y 5204 + 1300*x 5205 5206 x + y 10 8 6 2 4 3 2 4 5 4 12 5207 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5208 5209 x + y 5210 - 315*x 5211 5212 x + y 10 8 6 2 4 3 2 4 5 4 8 5213 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5214 5215 x + y 5216 - 160*x 5217 5218 x + y 10 8 6 2 4 3 2 4 5 4 7 5219 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5220 5221 x + y 5222 + 50*x 5223 5224 x + y 10 8 6 2 4 3 2 4 5 4 3 5225 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5226 5227 x + y 5228 - 120*x 5229 5230 x + y 10 8 6 2 4 3 2 4 5 4 2 5231 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5232 5233 x + y 5234 + 70*x 5235 5236 x + y 10 8 6 2 4 3 2 4 5 3 13 5237 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5238 5239 x + y 5240 - 90*x 5241 5242 x + y 10 8 6 2 4 3 2 4 5 3 8 5243 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5244 5245 x + y 5246 + 40*x 5247 5248 x + y 10 8 6 2 4 3 2 4 5 3 3 5249 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5250 5251 x + y 5252 + 70*x 5253 5254 x + y 10 8 6 2 4 3 2 4 5 2 14 5255 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5256 5257 x + y 5258 + 100*x 5259 5260 x + y 10 8 6 2 4 3 2 4 5 2 13 5261 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5262 5263 x + y 5264 - 80*x 5265 5266 x + y 10 8 6 2 4 3 2 4 5 2 9 5267 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5268 5269 x + y 5270 - 20*x 5271 5272 x + y 10 8 6 2 4 3 2 4 5 2 8 5273 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5274 5275 x + y 5276 + 35*x 5277 5278 x + y 10 8 6 2 4 3 2 4 5 2 4 5279 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5280 5281 x + y 5282 - 40*x 5283 5284 x + y 10 8 6 2 4 3 2 4 5 2 3 5285 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5286 5287 x + y 5288 + 5*x 5289 5290 x + y 10 8 6 2 4 3 2 4 5 14 5291 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y 5292 5293 x + y 5294 - 10*x 5295 5296 x + y 10 8 6 2 4 3 2 4 5 9 5297 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 5298 5299 x + y 5300 10*x 5301 5302 x + y 10 8 6 2 4 3 2 4 5 4 5303 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 5304 5305 x + y 5306 5*x 5307 5308 x + y 10 8 6 2 4 3 2 4 5 15 5309 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y - 5310 5311 x + y 5312 9*x 5313 5314 x + y 10 8 6 2 4 3 2 4 5 10 5315 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 5316 5317 x + y 5318 9*x 5319 5320 x + y 10 8 6 2 4 3 2 4 5 5 5321 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 5322 5323 x + y x + y 10 8 6 2 4 3 2 4 5 5324 x *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5325 5326 2 11 x + y 5327 *log(x) *x + 5*x 5328 5329 x + y 10 8 6 2 4 3 2 4 5 5330 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5331 5332 2 9 x + y 5333 *log(x) *x *y + 10*x 5334 5335 x + y 10 8 6 2 4 3 2 4 5 5336 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5337 5338 2 7 2 x + y 5339 *log(x) *x *y + 10*x 5340 5341 x + y 10 8 6 2 4 3 2 4 5 5342 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5343 5344 2 5 3 x + y 5345 *log(x) *x *y + 5*x 5346 5347 x + y 10 8 6 2 4 3 2 4 5 5348 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5349 5350 2 3 4 x + y 5351 *log(x) *x *y + x 5352 5353 x + y 10 8 6 2 4 3 2 4 5 5354 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5355 5356 2 5 x + y 5357 *log(x) *x*y + 20*x 5358 5359 x + y 10 8 6 2 4 3 2 4 5 5360 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5361 5362 20 x + y 5363 *x + 10*x 5364 5365 x + y 10 8 6 2 4 3 2 4 5 5366 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5367 5368 19 x + y 5369 *x + 180*x 5370 5371 x + y 10 8 6 2 4 3 2 4 5 5372 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5373 5374 18 x + y 5375 *x *y + 90*x 5376 5377 x + y 10 8 6 2 4 3 2 4 5 5378 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5379 5380 17 x + y 5381 *x *y + 720*x 5382 5383 x + y 10 8 6 2 4 3 2 4 5 5384 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5385 5386 16 2 x + y 5387 *x *y + 360*x 5388 5389 x + y 10 8 6 2 4 3 2 4 5 5390 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5391 5392 15 2 x + y 5393 *x *y + 1680*x 5394 5395 x + y 10 8 6 2 4 3 2 4 5 5396 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5397 5398 14 3 x + y 5399 *x *y + 840*x 5400 5401 x + y 10 8 6 2 4 3 2 4 5 5402 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5403 5404 13 3 x + y 5405 *x *y + 2520*x 5406 5407 x + y 10 8 6 2 4 3 2 4 5 5408 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5409 5410 12 4 x + y 5411 *x *y + 1260*x 5412 5413 x + y 10 8 6 2 4 3 2 4 5 5414 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5415 5416 11 4 x + y 5417 *x *y + x 5418 5419 x + y 10 8 6 2 4 3 2 4 5 5420 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5421 5422 11 x + y 5423 *x + 2520*x 5424 5425 x + y 10 8 6 2 4 3 2 4 5 5426 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5427 5428 10 5 x + y 5429 *x *y + x 5430 5431 x + y 10 8 6 2 4 3 2 4 5 5432 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5433 5434 10 x + y 5435 *x *y - 40*x 5436 5437 x + y 10 8 6 2 4 3 2 4 5 5438 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5439 5440 10 x + y 5441 *x + 1260*x 5442 5443 x + y 10 8 6 2 4 3 2 4 5 5444 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5445 5446 9 5 x + y 5447 *x *y + 5*x 5448 5449 x + y 10 8 6 2 4 3 2 4 5 5450 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5451 5452 9 x + y 5453 *x *y - 20*x 5454 5455 x + y 10 8 6 2 4 3 2 4 5 5456 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5457 5458 9 x + y 5459 *x + 1680*x 5460 5461 x + y 10 8 6 2 4 3 2 4 5 5462 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5463 5464 8 6 x + y 5465 *x *y + 5*x 5466 5467 x + y 10 8 6 2 4 3 2 4 5 5468 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5469 5470 8 2 x + y 5471 *x *y - 160*x 5472 5473 x + y 10 8 6 2 4 3 2 4 5 5474 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5475 5476 8 x + y 5477 *x *y + 840*x 5478 5479 x + y 10 8 6 2 4 3 2 4 5 5480 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5481 5482 7 6 x + y 5483 *x *y + 10*x 5484 5485 x + y 10 8 6 2 4 3 2 4 5 5486 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5487 5488 7 2 x + y 5489 *x *y - 80*x 5490 5491 x + y 10 8 6 2 4 3 2 4 5 5492 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5493 5494 7 x + y 5495 *x *y + 720*x 5496 5497 x + y 10 8 6 2 4 3 2 4 5 5498 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5499 5500 6 7 x + y 5501 *x *y + 10*x 5502 5503 x + y 10 8 6 2 4 3 2 4 5 5504 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5505 5506 6 3 x + y 5507 *x *y - 240*x 5508 5509 x + y 10 8 6 2 4 3 2 4 5 5510 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5511 5512 6 2 x + y 5513 *x *y + 360*x 5514 5515 x + y 10 8 6 2 4 3 2 4 5 5516 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5517 5518 5 7 x + y 5519 *x *y + 10*x 5520 5521 x + y 10 8 6 2 4 3 2 4 5 5522 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5523 5524 5 3 x + y 5525 *x *y - 120*x 5526 5527 x + y 10 8 6 2 4 3 2 4 5 5528 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5529 5530 5 2 x + y 5531 *x *y + 180*x 5532 5533 x + y 10 8 6 2 4 3 2 4 5 5534 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5535 5536 4 8 x + y 5537 *x *y + 10*x 5538 5539 x + y 10 8 6 2 4 3 2 4 5 5540 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5541 5542 4 4 x + y 5543 *x *y - 160*x 5544 5545 x + y 10 8 6 2 4 3 2 4 5 5546 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5547 5548 4 3 x + y 5549 *x *y + 90*x 5550 5551 x + y 10 8 6 2 4 3 2 4 5 5552 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5553 5554 3 8 x + y 5555 *x *y + 5*x 5556 5557 x + y 10 8 6 2 4 3 2 4 5 5558 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5559 5560 3 4 x + y 5561 *x *y - 80*x 5562 5563 x + y 10 8 6 2 4 3 2 4 5 5564 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5565 5566 3 3 x + y 5567 *x *y + 20*x 5568 5569 x + y 10 8 6 2 4 3 2 4 5 5570 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5571 5572 2 9 x + y 5573 *x *y + 5*x 5574 5575 x + y 10 8 6 2 4 3 2 4 5 5576 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5577 5578 2 5 x + y 5579 *x *y - 40*x 5580 5581 x + y 10 8 6 2 4 3 2 4 5 5582 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5583 5584 2 4 x + y 5585 *x *y + 10*x 5586 5587 x + y 10 8 6 2 4 3 2 4 5 5588 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5589 5590 9 x + y 5591 *x*y + x 5592 5593 x + y 10 8 6 2 4 3 2 4 5 5594 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5595 5596 5 x + y 5597 *x*y - 20*x 5598 5599 x + y 10 8 6 2 4 3 2 4 5 5600 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5601 5602 4 x + y 5603 *x*y + x 5604 5605 x + y 10 8 6 2 4 3 2 4 5 5606 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5607 5608 6 x + y 5609 *y + 10*x 5610 5611 x + y 10 8 6 2 4 3 2 4 5 19 5612 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5613 5614 x + y 5615 10*x 5616 5617 x + y 10 8 6 2 4 3 2 4 5 18 5618 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5619 5620 x + y 5621 + 100*x 5622 5623 x + y 10 8 6 2 4 3 2 4 5 18 5624 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5625 5626 x + y 5627 90*x 5628 5629 x + y 10 8 6 2 4 3 2 4 5 17 5630 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5631 5632 x + y 5633 + 90*x 5634 5635 x + y 10 8 6 2 4 3 2 4 5 16 2 5636 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5637 5638 x + y 5639 + 800*x 5640 5641 x + y 10 8 6 2 4 3 2 4 5 16 5642 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5643 5644 x + y 5645 + 360*x 5646 5647 x + y 10 8 6 2 4 3 2 4 5 15 2 5648 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5649 5650 x + y 5651 + 360*x 5652 5653 x + y 10 8 6 2 4 3 2 4 5 14 3 5654 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5655 5656 x + y 5657 + 2800*x 5658 5659 x + y 10 8 6 2 4 3 2 4 5 14 2 5660 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5661 5662 x + y 5663 + 840*x 5664 5665 x + y 10 8 6 2 4 3 2 4 5 13 3 5666 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5667 5668 x + y 5669 + 840*x 5670 5671 x + y 10 8 6 2 4 3 2 4 5 12 4 5672 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5673 5674 x + y 5675 + 5600*x 5676 5677 x + y 10 8 6 2 4 3 2 4 5 12 3 5678 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5679 5680 x + y 5681 + 1260*x 5682 5683 x + y 10 8 6 2 4 3 2 4 5 11 4 5684 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5685 5686 x + y 5687 + 1260*x 5688 5689 x + y 10 8 6 2 4 3 2 4 5 10 5 5690 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5691 5692 x + y 5693 + 7000*x 5694 5695 x + y 10 8 6 2 4 3 2 4 5 10 4 5696 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5697 5698 x + y 5699 + x 5700 5701 x + y 10 8 6 2 4 3 2 4 5 10 5702 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5703 5704 x + y 5705 1260*x 5706 5707 x + y 10 8 6 2 4 3 2 4 5 9 5 5708 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5709 5710 x + y 5711 - 20*x 5712 5713 x + y 10 8 6 2 4 3 2 4 5 9 5714 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5715 5716 x + y 5717 1260*x 5718 5719 x + y 10 8 6 2 4 3 2 4 5 8 6 5720 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5721 5722 x + y 5723 + 5600*x 5724 5725 x + y 10 8 6 2 4 3 2 4 5 8 5 5726 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5727 5728 x + y 5729 - 15*x 5730 5731 x + y 10 8 6 2 4 3 2 4 5 8 5732 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5733 5734 x + y 5735 40*x 5736 5737 x + y 10 8 6 2 4 3 2 4 5 8 5738 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5739 5740 x + y 5741 840*x 5742 5743 x + y 10 8 6 2 4 3 2 4 5 7 6 5744 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5745 5746 x + y 5747 - 80*x 5748 5749 x + y 10 8 6 2 4 3 2 4 5 7 5750 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5751 5752 x + y 5753 840*x 5754 5755 x + y 10 8 6 2 4 3 2 4 5 6 7 5756 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5757 5758 x + y 5759 + 2800*x 5760 5761 x + y 10 8 6 2 4 3 2 4 5 6 6 5762 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5763 5764 x + y 5765 - 70*x 5766 5767 x + y 10 8 6 2 4 3 2 4 5 6 2 5768 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5769 5770 x + y 5771 + 120*x 5772 5773 x + y 10 8 6 2 4 3 2 4 5 6 5774 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5775 5776 x + y 5777 360*x 5778 5779 x + y 10 8 6 2 4 3 2 4 5 5 7 5780 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5781 5782 x + y 5783 - 120*x 5784 5785 x + y 10 8 6 2 4 3 2 4 5 5 2 5786 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5787 5788 x + y 5789 + 360*x 5790 5791 x + y 10 8 6 2 4 3 2 4 5 4 8 5792 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5793 5794 x + y 5795 + 800*x 5796 5797 x + y 10 8 6 2 4 3 2 4 5 4 7 5798 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5799 5800 x + y 5801 - 110*x 5802 5803 x + y 10 8 6 2 4 3 2 4 5 4 3 5804 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5805 5806 x + y 5807 + 120*x 5808 5809 x + y 10 8 6 2 4 3 2 4 5 4 2 5810 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5811 5812 x + y 5813 + 90*x 5814 5815 x + y 10 8 6 2 4 3 2 4 5 3 8 5816 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5817 5818 x + y 5819 - 80*x 5820 5821 x + y 10 8 6 2 4 3 2 4 5 3 3 5822 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5823 5824 x + y 5825 + 90*x 5826 5827 x + y 10 8 6 2 4 3 2 4 5 2 9 5828 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5829 5830 x + y 5831 + 100*x 5832 5833 x + y 10 8 6 2 4 3 2 4 5 2 8 5834 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5835 5836 x + y 5837 - 75*x 5838 5839 x + y 10 8 6 2 4 3 2 4 5 2 4 5840 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5841 5842 x + y 5843 + 40*x 5844 5845 x + y 10 8 6 2 4 3 2 4 5 2 3 5846 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5847 5848 x + y 5849 + 10*x 5850 5851 x + y 10 8 6 2 4 3 2 4 5 9 5852 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y - 5853 5854 x + y 5855 20*x 5856 5857 x + y 10 8 6 2 4 3 2 4 5 4 5858 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 5859 5860 x + y 5861 10*x 5862 5863 x + y 10 8 6 2 4 3 2 4 5 10 5864 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y - 5865 5866 x + y 5867 19*x 5868 5869 x + y 10 8 6 2 4 3 2 4 5 5 5870 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 5871 5872 x + y 5873 20*x 5874 5875 x + y 10 8 6 2 4 3 2 4 5 5876 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5877 5878 10 x + y 5879 *x + 10*x 5880 5881 x + y 10 8 6 2 4 3 2 4 5 5882 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5883 5884 9 x + y 5885 *x + 80*x 5886 5887 x + y 10 8 6 2 4 3 2 4 5 5888 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5889 5890 8 x + y 5891 *x *y + 40*x 5892 5893 x + y 10 8 6 2 4 3 2 4 5 5894 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5895 5896 7 x + y 5897 *x *y + 120*x 5898 5899 x + y 10 8 6 2 4 3 2 4 5 5900 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5901 5902 6 2 x + y 5903 *x *y + 60*x 5904 5905 x + y 10 8 6 2 4 3 2 4 5 5906 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5907 5908 5 2 x + y 5909 *x *y + 80*x 5910 5911 x + y 10 8 6 2 4 3 2 4 5 5912 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5913 5914 4 3 x + y 5915 *x *y + 40*x 5916 5917 x + y 10 8 6 2 4 3 2 4 5 5918 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5919 5920 3 3 x + y 5921 *x *y + 20*x 5922 5923 x + y 10 8 6 2 4 3 2 4 5 5924 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5925 5926 2 4 x + y 5927 *x *y + 10*x 5928 5929 x + y 10 8 6 2 4 3 2 4 5 5930 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 5931 5932 4 x + y 5933 *x*y + 10*x 5934 5935 x + y 10 8 6 2 4 3 2 4 5 9 5936 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 5937 5938 x + y 5939 10*x 5940 5941 x + y 10 8 6 2 4 3 2 4 5 8 5942 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5943 5944 x + y 5945 40*x 5946 5947 x + y 10 8 6 2 4 3 2 4 5 7 5948 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 5949 5950 x + y 5951 40*x 5952 5953 x + y 10 8 6 2 4 3 2 4 5 6 2 5954 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5955 5956 x + y 5957 + 60*x 5958 5959 x + y 10 8 6 2 4 3 2 4 5 5 2 5960 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5961 5962 x + y 5963 + 60*x 5964 5965 x + y 10 8 6 2 4 3 2 4 5 4 3 5966 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5967 5968 x + y 5969 + 40*x 5970 5971 x + y 10 8 6 2 4 3 2 4 5 3 3 5972 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5973 5974 x + y 5975 + 40*x 5976 5977 x + y 10 8 6 2 4 3 2 4 5 2 4 5978 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 5979 5980 x + y 5981 + 10*x 5982 5983 x + y 10 8 6 2 4 3 2 4 5 4 5984 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y + 5985 5986 x + y 5987 10*x 5988 5989 x + y 10 8 6 2 4 3 2 4 5 5 5990 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 5991 5992 x + y 10 8 6 2 4 3 2 4 5 38 5993 50*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 5994 5995 x + y 10 8 6 2 4 3 2 4 5 5996 + 900*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 5997 5998 36 5999 *x *y + 7650 6000 6001 x + y 10 8 6 2 4 3 2 4 5 34 2 6002 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6003 6004 + 40800 6005 6006 x + y 10 8 6 2 4 3 2 4 5 32 3 6007 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6008 6009 + 153000 6010 6011 x + y 10 8 6 2 4 3 2 4 5 30 4 6012 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6013 6014 + 428400 6015 6016 x + y 10 8 6 2 4 3 2 4 5 28 5 6017 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6018 6019 x + y 10 8 6 2 4 3 2 4 5 6020 - 60*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6021 6022 28 6023 *x + 928200 6024 6025 x + y 10 8 6 2 4 3 2 4 5 26 6 6026 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6027 6028 x + y 10 8 6 2 4 3 2 4 5 6029 - 780*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6030 6031 26 6032 *x *y + 1591200 6033 6034 x + y 10 8 6 2 4 3 2 4 5 24 7 6035 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6036 6037 x + y 10 8 6 2 4 3 2 4 5 6038 - 4680*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6039 6040 24 2 6041 *x *y + 2187900 6042 6043 x + y 10 8 6 2 4 3 2 4 5 22 8 6044 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6045 6046 - 17160 6047 6048 x + y 10 8 6 2 4 3 2 4 5 22 3 6049 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6050 6051 + 2431000 6052 6053 x + y 10 8 6 2 4 3 2 4 5 20 9 6054 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6055 6056 - 42900 6057 6058 x + y 10 8 6 2 4 3 2 4 5 20 4 6059 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6060 6061 + 2187900 6062 6063 x + y 10 8 6 2 4 3 2 4 5 18 6064 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6065 6066 10 6067 *y - 77220 6068 6069 x + y 10 8 6 2 4 3 2 4 5 18 5 6070 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6071 6072 x + y 10 8 6 2 4 3 2 4 5 6073 + 60*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6074 6075 18 6076 *x + 1591200 6077 6078 x + y 10 8 6 2 4 3 2 4 5 16 6079 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6080 6081 11 6082 *y - 102960 6083 6084 x + y 10 8 6 2 4 3 2 4 5 16 6 6085 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6086 6087 x + y 10 8 6 2 4 3 2 4 5 6088 + 480*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6089 6090 16 6091 *x *y + 928200 6092 6093 x + y 10 8 6 2 4 3 2 4 5 14 6094 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6095 6096 12 6097 *y - 102960 6098 6099 x + y 10 8 6 2 4 3 2 4 5 14 7 6100 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6101 6102 x + y 10 8 6 2 4 3 2 4 5 6103 + 1680*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6104 6105 14 2 6106 *x *y + 428400 6107 6108 x + y 10 8 6 2 4 3 2 4 5 12 6109 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6110 6111 13 6112 *y - 77220 6113 6114 x + y 10 8 6 2 4 3 2 4 5 12 8 6115 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6116 6117 x + y 10 8 6 2 4 3 2 4 5 6118 + 3360*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6119 6120 12 3 6121 *x *y + 153000 6122 6123 x + y 10 8 6 2 4 3 2 4 5 10 6124 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6125 6126 14 6127 *y - 42900 6128 6129 x + y 10 8 6 2 4 3 2 4 5 10 9 6130 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6131 6132 x + y 10 8 6 2 4 3 2 4 5 6133 + 4200*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6134 6135 10 4 6136 *x *y + 40800 6137 6138 x + y 10 8 6 2 4 3 2 4 5 8 15 6139 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6140 6141 - 17160 6142 6143 x + y 10 8 6 2 4 3 2 4 5 8 10 6144 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6145 6146 x + y 10 8 6 2 4 3 2 4 5 6147 + 3360*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6148 6149 8 5 6150 *x *y + 7650 6151 6152 x + y 10 8 6 2 4 3 2 4 5 6 16 6153 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6154 6155 x + y 10 8 6 2 4 3 2 4 5 6156 - 4680*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6157 6158 6 11 6159 *x *y + 1680 6160 6161 x + y 10 8 6 2 4 3 2 4 5 6 6 6162 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6163 6164 x + y 10 8 6 2 4 3 2 4 5 6165 + 900*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6166 6167 4 17 6168 *x *y - 780 6169 6170 x + y 10 8 6 2 4 3 2 4 5 4 12 6171 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6172 6173 x + y 10 8 6 2 4 3 2 4 5 6174 + 480*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6175 6176 4 7 6177 *x *y + 50 6178 6179 x + y 10 8 6 2 4 3 2 4 5 2 18 6180 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6181 6182 x + y 10 8 6 2 4 3 2 4 5 6183 - 60*kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6184 6185 2 13 6186 *x *y + 60 6187 6188 x + y 10 8 6 2 4 3 2 4 5 2 8 6189 *kummerm(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6190 6191 x + y 10 8 6 2 4 3 2 4 5 6192 + 100*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6193 6194 28 6195 *x + 1300 6196 6197 x + y 10 8 6 2 4 3 2 4 5 26 6198 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6199 6200 x + y 10 8 6 2 4 3 2 4 5 6201 + 7800*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6202 6203 24 2 6204 *x *y + 28600 6205 6206 x + y 10 8 6 2 4 3 2 4 5 22 3 6207 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6208 6209 + 71500 6210 6211 x + y 10 8 6 2 4 3 2 4 5 20 4 6212 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6213 6214 + 128700 6215 6216 x + y 10 8 6 2 4 3 2 4 5 18 5 6217 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6218 6219 x + y 10 8 6 2 4 3 2 4 5 6220 - 160*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6221 6222 18 6223 *x + 171600 6224 6225 x + y 10 8 6 2 4 3 2 4 5 16 6 6226 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6227 6228 x + y 10 8 6 2 4 3 2 4 5 6229 - 1280*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6230 6231 16 6232 *x *y + 171600 6233 6234 x + y 10 8 6 2 4 3 2 4 5 14 7 6235 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6236 6237 x + y 10 8 6 2 4 3 2 4 5 6238 - 4480*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6239 6240 14 2 6241 *x *y + 128700 6242 6243 x + y 10 8 6 2 4 3 2 4 5 12 8 6244 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6245 6246 x + y 10 8 6 2 4 3 2 4 5 6247 - 8960*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6248 6249 12 3 6250 *x *y + 71500 6251 6252 x + y 10 8 6 2 4 3 2 4 5 10 9 6253 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6254 6255 - 11200 6256 6257 x + y 10 8 6 2 4 3 2 4 5 10 4 6258 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6259 6260 + 28600 6261 6262 x + y 10 8 6 2 4 3 2 4 5 8 10 6263 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6264 6265 x + y 10 8 6 2 4 3 2 4 5 6266 - 8960*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6267 6268 8 5 6269 *x *y + 7800 6270 6271 x + y 10 8 6 2 4 3 2 4 5 6 11 6272 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6273 6274 x + y 10 8 6 2 4 3 2 4 5 6275 - 4480*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6276 6277 6 6 6278 *x *y + 1300 6279 6280 x + y 10 8 6 2 4 3 2 4 5 4 12 6281 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6282 6283 x + y 10 8 6 2 4 3 2 4 5 6284 - 1280*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6285 6286 4 7 6287 *x *y + 100 6288 6289 x + y 10 8 6 2 4 3 2 4 5 2 13 6290 *kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6291 6292 x + y 10 8 6 2 4 3 2 4 5 6293 - 160*kummerm(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6294 6295 2 8 6296 *x *y + 100 6297 6298 x + y 10 8 6 2 4 3 2 4 5 18 6299 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 6300 6301 x + y 10 8 6 2 4 3 2 4 5 16 6302 800*kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6303 6304 *y + 2800 6305 6306 x + y 10 8 6 2 4 3 2 4 5 14 2 6307 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6308 6309 x + y 10 8 6 2 4 3 2 4 5 6310 + 5600*kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6311 6312 12 3 6313 *x *y + 7000 6314 6315 x + y 10 8 6 2 4 3 2 4 5 10 4 6316 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6317 6318 x + y 10 8 6 2 4 3 2 4 5 6319 + 5600*kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6320 6321 8 5 6322 *x *y + 2800 6323 6324 x + y 10 8 6 2 4 3 2 4 5 6 6 6325 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6326 6327 x + y 10 8 6 2 4 3 2 4 5 6328 + 800*kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6329 6330 4 7 6331 *x *y + 100 6332 6333 x + y 10 8 6 2 4 3 2 4 5 2 8 6334 *kummerm(0,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y ) 6335 6336 2*x + 2*y x + y 10 x + y 8 x + y 6 2 6337/(x*(x + 2*x *x + 10*x *x *y + 20*x *x *y 6338 6339 x + y 4 3 x + y 2 4 x + y 5 20 18 6340 + 20*x *x *y + 10*x *x *y + 2*x *y + x + 10*x *y 6341 6342 16 2 14 3 12 4 10 5 8 6 6 7 6343 + 45*x *y + 120*x *y + 210*x *y + 252*x *y + 210*x *y + 120*x *y 6344 6345 4 8 2 9 10 6346 + 45*x *y + 10*x *y + y )) 6347 6348df(KummerU(a,b,z),x); 6349 6350 6351 2*x + 2*y 6352(x 6353 6354 x + y 10 8 6 2 4 3 2 4 5 6355 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6356 6357 2*x + 2*y 6358 *x + x 6359 6360 x + y 10 8 6 2 4 3 2 4 5 6361 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 6362 6363 2*x + 2*y 6364 x 6365 6366 x + y 10 8 6 2 4 3 2 4 5 6367 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y + 6368 6369 x + y x + y 10 8 6 2 4 3 2 4 5 6370 x *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6371 6372 11 x + y 6373 *log(x)*x + 5*x 6374 6375 x + y 10 8 6 2 4 3 2 4 5 6376 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6377 6378 9 x + y 6379 *x *y + 10*x 6380 6381 x + y 10 8 6 2 4 3 2 4 5 6382 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6383 6384 7 2 x + y 6385 *x *y + 10*x 6386 6387 x + y 10 8 6 2 4 3 2 4 5 6388 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6389 6390 5 3 x + y 6391 *x *y + 5*x 6392 6393 x + y 10 8 6 2 4 3 2 4 5 6394 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6395 6396 3 4 x + y 6397 *x *y + x 6398 6399 x + y 10 8 6 2 4 3 2 4 5 6400 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6401 6402 5 x + y 6403 *x*y - x 6404 6405 x + y 10 8 6 2 4 3 2 4 5 6406 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6407 6408 x + y 6409 *x + x 6410 6411 x + y 10 8 6 2 4 3 2 4 5 11 6412 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 6413 6414 x + y x + y 10 8 6 2 4 3 2 4 5 6415 x *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6416 6417 10 x + y 6418 *x *y + 10*x 6419 6420 x + y 10 8 6 2 4 3 2 4 5 10 6421 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x + 6422 6423 x + y 6424 5*x 6425 6426 x + y 10 8 6 2 4 3 2 4 5 9 6427 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 6428 6429 x + y 6430 5*x 6431 6432 x + y 10 8 6 2 4 3 2 4 5 8 2 6433 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6434 6435 x + y 6436 + 40*x 6437 6438 x + y 10 8 6 2 4 3 2 4 5 8 6439 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y + 6440 6441 x + y 6442 10*x 6443 6444 x + y 10 8 6 2 4 3 2 4 5 7 2 6445 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6446 6447 x + y 6448 + 10*x 6449 6450 x + y 10 8 6 2 4 3 2 4 5 6 3 6451 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6452 6453 x + y 6454 + 60*x 6455 6456 x + y 10 8 6 2 4 3 2 4 5 6 2 6457 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6458 6459 x + y 6460 + 10*x 6461 6462 x + y 10 8 6 2 4 3 2 4 5 5 3 6463 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6464 6465 x + y 6466 + 10*x 6467 6468 x + y 10 8 6 2 4 3 2 4 5 4 4 6469 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6470 6471 x + y 6472 + 40*x 6473 6474 x + y 10 8 6 2 4 3 2 4 5 4 3 6475 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6476 6477 x + y 6478 + 5*x 6479 6480 x + y 10 8 6 2 4 3 2 4 5 3 4 6481 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6482 6483 x + y 6484 + 5*x 6485 6486 x + y 10 8 6 2 4 3 2 4 5 2 5 6487 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6488 6489 x + y 6490 + 10*x 6491 6492 x + y 10 8 6 2 4 3 2 4 5 2 4 6493 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6494 6495 x + y 6496 + x 6497 6498 x + y 10 8 6 2 4 3 2 4 5 5 6499 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x*y - 6500 6501 x + y x + y 10 8 6 2 4 3 2 4 5 6502 x *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6503 6504 x + y 6505 *x + x 6506 6507 x + y 10 8 6 2 4 3 2 4 5 6 6508 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*y - 6509 6510 x + y x + y 10 8 6 2 4 3 2 4 5 6511 x *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6512 6513 x + y 6514 *y - x 6515 6516 x + y 10 8 6 2 4 3 2 4 5 6517 *kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*log(x) 6518 6519 x + y 6520 *x - x 6521 6522 x + y 10 8 6 2 4 3 2 4 5 6523 *kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x - 6524 6525 x + y x + y 10 8 6 2 4 3 2 4 5 6526 x *kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6527 6528 x + y 10 8 6 2 4 3 2 4 5 6529 *y + 10*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6530 6531 20 6532 *x + 90 6533 6534 x + y 10 8 6 2 4 3 2 4 5 18 6535 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6536 6537 x + y 10 8 6 2 4 3 2 4 5 6538 + 360*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6539 6540 16 2 6541 *x *y + 840 6542 6543 x + y 10 8 6 2 4 3 2 4 5 14 3 6544 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6545 6546 x + y 10 8 6 2 4 3 2 4 5 6547 + 1260*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6548 6549 12 4 6550 *x *y + 1260 6551 6552 x + y 10 8 6 2 4 3 2 4 5 10 5 6553 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6554 6555 x + y 10 8 6 2 4 3 2 4 5 6556 - 10*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6557 6558 10 6559 *x + 840 6560 6561 x + y 10 8 6 2 4 3 2 4 5 8 6 6562 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6563 6564 x + y 10 8 6 2 4 3 2 4 5 8 6565 - 40*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6566 6567 *y + 360 6568 6569 x + y 10 8 6 2 4 3 2 4 5 6 7 6570 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6571 6572 x + y 10 8 6 2 4 3 2 4 5 6 6573 - 60*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6574 6575 2 6576 *y + 90 6577 6578 x + y 10 8 6 2 4 3 2 4 5 4 8 6579 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6580 6581 x + y 10 8 6 2 4 3 2 4 5 4 6582 - 40*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6583 6584 3 6585 *y + 10 6586 6587 x + y 10 8 6 2 4 3 2 4 5 2 9 6588 *kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6589 6590 x + y 10 8 6 2 4 3 2 4 5 2 6591 - 10*kummeru(2,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6592 6593 4 6594 *y - 10 6595 6596 x + y 10 8 6 2 4 3 2 4 5 10 6597 *kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x - 6598 6599 x + y 10 8 6 2 4 3 2 4 5 8 6600 40*kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6601 6602 x + y 10 8 6 2 4 3 2 4 5 6603 - 60*kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y ) 6604 6605 6 2 6606 *x *y - 40 6607 6608 x + y 10 8 6 2 4 3 2 4 5 4 3 6609 *kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x *y 6610 6611 x + y 10 8 6 2 4 3 2 4 5 2 6612 - 10*kummeru(1,3,x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )*x 6613 6614 4 x + y 10 8 6 2 4 3 2 4 5 6615 *y )/(x*(x + x + 5*x *y + 10*x *y + 10*x *y + 5*x *y + y )) 6616 6617 6618 6619 6620% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 6621 6622% 9. Bessel functions 6623 6624% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 6625 6626 6627% Lengthy test of the Bessel functions. This isn't even 6628% remotely exhaustive of the special cases -- though a 6629% real person with lots of time could no doubt come up 6630% with a better lot of tests than this automated rubbish. 6631% Again, compromise by only actually doing one in five or 6632% nine. If you want a really thorough test, you can 6633% easily change this to get it; but it'll take hours to 6634% run. 6635 6636clear p, q; 6637 6638 6639 6640hankel1(p,q); 6641 6642 6643hankel1(p,q) 6644 6645r := df(ws,q); 6646 6647 6648 hankel1(p - 1,q)*q - hankel1(p,q)*p 6649r := ------------------------------------- 6650 q 6651 6652 6653on complex; 6654 6655 6656 6657r; 6658 6659 6660 besselj(p - 1,q)*q - besselj(p,q)*p + i*bessely(p - 1,q)*q - i*bessely(p,q)*p 6661------------------------------------------------------------------------------- 6662 q 6663 6664p:=3/8; 6665 6666 6667 3 6668p := --- 6669 8 6670 6671r; 6672 6673 6674 - 5 3*pi - 5 3*pi 6675(8*i*besselj(------,q)*cos(------)*q + 8*besselj(------,q)*sin(------)*q 6676 8 8 8 8 6677 6678 - 3 5 6679 + 3*i*besselj(------,q) + 8*i*besselj(---,q)*q 6680 8 8 6681 6682 3 3*pi 3 3*pi 6683 - 3*i*besselj(---,q)*cos(------) - 3*besselj(---,q)*sin(------))/(8 6684 8 8 8 8 6685 6686 3*pi 6687 *sin(------)*q) 6688 8 6689 6690q := pi; 6691 6692 6693q := pi 6694 6695r; 6696 6697 6698 - 5 3*pi - 5 3*pi 6699(8*i*besselj(------,pi)*cos(------)*pi + 8*besselj(------,pi)*sin(------)*pi 6700 8 8 8 8 6701 6702 - 3 5 6703 + 3*i*besselj(------,pi) + 8*i*besselj(---,pi)*pi 6704 8 8 6705 6706 3 3*pi 3 3*pi 6707 - 3*i*besselj(---,pi)*cos(------) - 3*besselj(---,pi)*sin(------))/(8 6708 8 8 8 8 6709 6710 3*pi 6711 *sin(------)*pi) 6712 8 6713 6714 6715on rounded; 6716 6717 6718*** Domain mode complex changed to complex-rounded 6719 6720 6721r; 6722 6723 6724 - 0.119366207318921501826662822529 6725 6726*hankel1(0.375,3.14159265358979323846264338328) 6727 6728 + hankel1( - 0.625,3.14159265358979323846264338328) 6729 6730 6731off complex, rounded; 6732 6733 6734*** Domain mode complex-rounded changed to rounded 6735 6736 6737df(df(BesselJ(pp,qq)+rr * hankel1(pp*2,qq) * 6738 BesselY(pp-qq,qq),qq),qq); 6739 6740 6741 2 6742(besselj(pp - 2,qq)*qq - 2*besselj(pp - 1,qq)*pp*qq + besselj(pp - 1,qq)*qq 6743 6744 2 6745 + besselj(pp,qq)*pp + besselj(pp,qq)*pp 6746 6747 2 6748 + bessely(pp - qq,qq)*hankel1(2*pp - 2,qq)*qq *rr 6749 6750 - 4*bessely(pp - qq,qq)*hankel1(2*pp - 1,qq)*pp*qq*rr 6751 6752 + bessely(pp - qq,qq)*hankel1(2*pp - 1,qq)*qq*rr 6753 6754 2 6755 + 4*bessely(pp - qq,qq)*hankel1(2*pp,qq)*pp *rr 6756 6757 + 2*bessely(pp - qq,qq)*hankel1(2*pp,qq)*pp*rr 6758 6759 2 6760 + df(bessely(pp - qq,qq),qq,2)*hankel1(2*pp,qq)*qq *rr 6761 6762 2 6763 + 2*df(bessely(pp - qq,qq),qq)*hankel1(2*pp - 1,qq)*qq *rr 6764 6765 2 6766 - 4*df(bessely(pp - qq,qq),qq)*hankel1(2*pp,qq)*pp*qq*rr)/qq 6767 6768 6769% Possible values for real args 6770t!*bes!*vr := { 1, pi, -pi, 26 }$ 6771 6772 6773 6774% Possible values for real and imaginary parts of complex args 6775t!*bes!*vc := { 0, 3, -41/2 }$ 6776 6777 6778 6779array s!*bes(4)$ 6780 6781 6782 6783s!*bes(1) := "BesselJ"$ 6784 6785 6786s!*bes(2) := "BesselY"$ 6787 6788 6789s!*bes(3) := "BesselI"$ 6790 6791 6792s!*bes(4) := "BesselK"$ 6793 6794 6795 6796pre := 16; 6797 6798 6799pre := 16 6800 6801precision pre; 6802 6803 680430 6805 6806preord := 10**pre; 6807 6808 6809preord := 10000000000000000 6810 6811t!*b!*c := 3; 6812 6813 6814t*b*c := 3 6815 6816 6817algebraic procedure do!*one!*bessel(s,n,z); 6818 (if s = 1 then BesselJ(n,z) 6819 else if s = 2 then BesselY(n,z) 6820 else if s = 3 then BesselI(n,z) 6821 else BesselK(n,z)); 6822 6823 6824do*one*bessel 6825 6826 6827algebraic procedure pr!*bessel(s,n,z,k); 6828 << if t!*b!*c = k 6829 then 6830 << on rounded; 6831 bes1 := do!*one!*bessel(s,n,z); 6832 precision(pre+5); 6833 bes2 := do!*one!*bessel(s,n,z); 6834 if bes1 neq 0 6835 then disc := floor abs(100*(bes2-bes1)*preord/bes1) 6836 else disc := 0; 6837 precision pre; 6838 write s!*bes(s), "(", n, ",", z, ") = ", bes1; 6839 if not numberp disc then 6840 << precom := !*complex; 6841 on complex; 6842 disc := disc; 6843 if not precom then off complex >>; 6844 if disc neq 0 6845 then write " (discrepancy ", disc, "% of one s.f.)"; 6846 if numberp disc and disc > 200 then 6847 << write "***** WARNING Significant Inaccuracy."; 6848 write " Lower precision result:"; 6849 write " ", bes1; 6850 write " Higher precision result:"; 6851 precision(pre+5); write " ", bes2; precision pre >>; 6852 off rounded; 6853 t!*b!*c := 0 >>; 6854 t!*b!*c := t!*b!*c + 1 >>; 6855 6856 6857pr*bessel 6858 6859 6860% About to begin Bessel test. We have a list of possible 6861% values, and we test every Bessel, with every value on the 6862% list as both order and argument. Every Bessel is computed 6863% twice, to different precisions (differing by 3), and any 6864% discrepancy is reported. The value reported is the diff- 6865% erence between the two computed values, expressed as a 6866% percentage of the unit of the least significant displayed 6867% digit. A discrepancy between 100% and 200% means that the 6868% last digit of the displayed value was found to differ at 6869% higher precision; values greater than 200% are cause for 6870% concern. An ideal discrepancy would be between about 1% 6871% and 20%; if the value is found to be zero, no discrepancy 6872% is reported. 6873 6874off msg; 6875 6876 6877 6878for s := 1:4 do 6879 << write(" ... Testing ", s!*bes(s), " for real domains ... "); 6880 for each n in t!*bes!*vr do 6881 for each z in t!*bes!*vr do 6882 pr!*bessel(s, n, z, 5) >>; 6883 6884 6885 ... Testing BesselJ for real domains ... 6886 6887BesselJ(1, - 3.141592653589793) = - 0.2846153431797528 6888 6889BesselJ(3.141592653589793,26) = - 0.006989220174690161 6890 6891 (discrepancy 5% of one s.f.) 6892 6893BesselJ(26,1) = 3.660826744416803e-35 6894 6895 ... Testing BesselY for real domains ... 6896 6897BesselY(1,3.141592653589793) = 0.358872916776719 6898 6899BesselY(3.141592653589793, - 3.141592653589793) = 6900 6901 6.283185307179586 6902 0.1545613960392598*( - 1.570796326794897) - 4.829362563540275 6903-------------------------------------------------------------------------------- 6904 3.141592653589793 6905 ( - 1.570796326794897) 6906 6907BesselY( - 3.141592653589793,26) = - 0.1386083623177915 6908 6909 ... Testing BesselI for real domains ... 6910 6911BesselI(1,1) = 0.565159103992485 6912 6913BesselI(3.141592653589793,3.141592653589793) = 1.011423335928613 6914 6915BesselI( - 3.141592653589793, - 3.141592653589793) = - 0.8856101155917482 6916 6917 + 0.4221616153281286*i 6918 6919BesselI(26,26) = 68397.86776155122 6920 6921 ... Testing BesselK for real domains ... 6922 6923BesselK(3.141592653589793,1) = 9.025908765806763 6924 6925BesselK( - 3.141592653589793,3.141592653589793) = 0.1107526602738113 6926 6927 (discrepancy 1% of one s.f.) 6928 6929BesselK(26, - 3.141592653589793) = besselk(26, - 3.141592653589793) 6930 6931 6932on complex; 6933 6934 6935 6936for s := 1:3 do 6937 << write (" ... Testing ", s!*bes(s), " for complex domains ... "); 6938 for each nr in t!*bes!*vc do 6939 for each ni in t!*bes!*vc do 6940 for each zr in t!*bes!*vc do 6941 for each zi in t!*bes!*vc do 6942 pr!*bessel(s, nr+ni*i, zr+zi*i, 9) >>; 6943 6944 6945 ... Testing BesselJ for complex domains ... 6946 6947BesselJ(0, - 20.5 + 3.0*i) = 1.05389016561334 + 1.410918160335249*i 6948 6949BesselJ(3*i, - 20.5 + 3.0*i) = 0.01225787392170983 + 0.01066256817009466*i 6950 6951BesselJ( - 20.5*i, - 20.5 + 3.0*i) = - 6.607837931625446e+38 6952 6953 + 7.203284455482089e+38*i 6954 6955BesselJ(3, - 20.5 + 3.0*i) = 1.568613483726435 - 0.7011991107137573*i 6956 6957BesselJ(3 + 3*i, - 20.5 + 3.0*i) = 0.007904103001381543 - 0.006566520928092784*i 6958 6959BesselJ(3.0 - 20.5*i, - 20.5 + 3.0*i) = - 7.069920310202644e+37 6960 6961 - 1.753271554229047e+37*i 6962 6963BesselJ( - 20.5, - 20.5 + 3.0*i) = 0.1758742246345278 - 0.332739860634916*i 6964 6965BesselJ( - 20.5 + 3.0*i, - 20.5 + 3.0*i) = 0.08815299110072903 6966 6967 - 0.1369698556512304*i 6968 6969BesselJ( - 20.5 - 20.5*i, - 20.5 + 3.0*i) = - 5.364748129151297e+46 6970 6971 + 2.608178375230083e+47*i 6972 6973 ... Testing BesselY for complex domains ... 6974 6975BesselY(0, - 20.5 + 3.0*i) = - 1.404746667469566 + 1.060048452645186*i 6976 6977BesselY(3*i, - 20.5 + 3.0*i) = 0.4973091982659732 + 0.7985114801567726*i 6978 6979BesselY( - 20.5*i, - 20.5 + 3.0*i) = - 7.203284455482089e+38 6980 6981 - 6.607837931625446e+38*i 6982 6983 (discrepancy 10% of one s.f.) 6984 6985BesselY(3, - 20.5 + 3.0*i) = 0.6963128100601111 + 1.576222640523309*i 6986 6987BesselY(3 + 3*i, - 20.5 + 3.0*i) = - 1.117333163968302 + 0.9789575771194796*i 6988 6989BesselY(3.0 - 20.5*i, - 20.5 + 3.0*i) = 1.753271554229047e+37 6990 6991 - 7.069920310202644e+37*i 6992 6993 (discrepancy 10% of one s.f.) 6994 6995BesselY( - 20.5, - 20.5 + 3.0*i) = 0.2353954565395826 + 0.144691313932682*i 6996 6997BesselY( - 20.5 + 3.0*i, - 20.5 + 3.0*i) = - 0.1527215881543493 6998 6999 + 0.2371137974094512*i 7000 7001BesselY( - 20.5 - 20.5*i, - 20.5 + 3.0*i) = - 2.608178375230083e+47 7002 7003 - 5.364748129151297e+46*i 7004 7005 (discrepancy 9% of one s.f.) 7006 7007 ... Testing BesselI for complex domains ... 7008 7009BesselI(0, - 20.5 + 3.0*i) = - 6.891185608459107e+7 - 1.506065792318474e+7*i 7010 7011BesselI(3*i, - 20.5 + 3.0*i) = - 6879.511500081906 - 1745.250262122384*i 7012 7013BesselI( - 20.5*i, - 20.5 + 3.0*i) = 4.756052726395977e+40 7014 7015 - 1.836844915663626e+40*i 7016 7017BesselI(3, - 20.5 + 3.0*i) = 5.56813934269752e+7 + 1.026348768124686e+7*i 7018 7019BesselI(3 + 3*i, - 20.5 + 3.0*i) = 5917.619873410601 - 1360.623977225443*i 7020 7021BesselI(3.0 - 20.5*i, - 20.5 + 3.0*i) = 1.125266362182384e+40 7022 7023 - 3.487618645712341e+39*i 7024 7025BesselI( - 20.5, - 20.5 + 3.0*i) = - 0.0005935206748136158 7026 7027 - 0.001045512507192035*i 7028 7029BesselI( - 20.5 + 3.0*i, - 20.5 + 3.0*i) = 0.0001367212493519011 7030 7031 - 0.00008899048591346719*i 7032 7033BesselI( - 20.5 - 20.5*i, - 20.5 + 3.0*i) = - 4.705541285798881e+45 7034 7035 + 6.968045629188714e+45*i 7036 7037 7038off complex; 7039 7040 7041 7042on msg; 7043 7044 7045 7046write (" ..."); 7047 7048 7049 ... 7050 7051write ("Bessel test complete."); 7052 7053 7054Bessel test complete. 7055 7056 7057 7058% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 7059 7060% 10. Incomplete Gamma and Beta functions (regularized) 7061 7062% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 7063 7064 7065igamma(3,0); 7066 7067 70680 7069 7070 7071igamma(1,1); 7072 7073 7074 e - 1 7075------- 7076 e 7077 7078 7079igamma(1,4); 7080 7081 7082 4 7083 e - 1 7084-------- 7085 4 7086 e 7087 7088 7089on rounded; 7090 7091 7092 7093igamma(1,1); 7094 7095 70960.6321205588285577 7097 7098 7099igamma(1,4); 7100 7101 71020.9816843611112658 7103 7104 7105igamma(2,4); 7106 7107 71080.9084218055563291 7109 7110 7111igamma(0.5,4); 7112 7113 71140.9953206825613376 7115 7116 7117ibeta(1,1,1); 7118 7119 71201 7121 7122 7123ibeta(1,2,1); 7124 7125 71261 7127 7128 7129ibeta(1,4,1); 7130 7131 71321 7133 7134 7135ibeta(2,4,1); 7136 7137 71381 7139 7140 7141ibeta(2,4,0.5); 7142 7143 71440.8125 7145 7146 7147ibeta(0.12,0.43,0.9); 7148 7149 71500.9114011367359803 7151 7152 7153precision 50; 7154 7155 715616 7157 7158 7159ibeta(0.12,0.43,0.9); 7160 7161 71620.91140113673598029129193960252752697713018702246564 7163 7164 7165precision 20; 7166 7167 716850 7169 7170 7171ibeta(0.12,0.43,0.9); 7172 7173 71740.91140113673598029129 7175 7176 7177on complex; 7178 7179 7180*** Domain mode rounded changed to complex-rounded 7181 7182 7183ibeta(1+i,1,1.5*i); 7184 7185 7186 - 0.12299596333468401978 + 0.28653674999354031595*i 7187 7188 7189off rounded,complex; 7190 7191 7192*** Domain mode complex-rounded changed to complex 7193 7194 7195ibeta(3,2,x); 7196 7197 7198 3 7199x *( - 3*x + 4) 7200 7201 7202precision reset; 7203 7204 720520 7206 7207 7208% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 7209 7210% 11. Exponential Integral, Sine and Cosine Integrals; 7211% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 7212 7213procedure do!*one!*int!:function(fn,n); 7214 write (fn," of ", n, " is ", 7215 if fn=!Ei then Ei(n) 7216 else if fn=!Si then Si(n) 7217 else if fn=!Ci then Ci(n) 7218 else if fn=!Shi then Shi(n) 7219 else if fn=!Chi then Chi(n) 7220 else if fn=!Fresnel_!S then Fresnel_S(n) 7221 else if fn=!Fresnel_!C then Fresnel_C(n) 7222 ); 7223 7224 7225do*one*int:function 7226 7227 7228% Ei(0), Ci(0), and Chi(0) are undefined 7229 7230Ei(0); 7231 7232 7233Ei(0) 7234 7235 7236Ci(0); 7237 7238 7239Ci(0) 7240 7241 7242Chi(0); 7243 7244 7245Chi(0) 7246 7247 7248on rounded; 7249 7250 7251 7252Ei(0); 7253 7254 7255***** Ei(0) is undefined 7256 7257 7258Ci(0); 7259 7260 7261***** Ci(0) is undefined 7262 7263 7264Chi(0); 7265 7266 7267***** Chi(0) is undefined 7268 7269 7270% Chi is undefined for negative real argument 7271 7272Chi(-1); 7273 7274 72753.14159265359*i + 0.83786694098 7276 7277 7278for x := 0.1 step 0.1 until 2.0 do 7279 do!*one!*int!:function(!Ei,x); 7280 7281 7282Ei of 0.1 is - 1.62281281397 7283 7284Ei of 0.2 is - 0.821760587902 7285 7286Ei of 0.3 is - 0.302668539266 7287 7288Ei of 0.4 is 0.104765218619 7289 7290Ei of 0.5 is 0.454219904863 7291 7292Ei of 0.6 is 0.769881289937 7293 7294Ei of 0.7 is 1.06490719462 7295 7296Ei of 0.8 is 1.34739654821 7297 7298Ei of 0.9 is 1.6228117137 7299 7300Ei of 1 is 1.89511781636 7301 7302Ei of 1.1 is 2.16737827956 7303 7304Ei of 1.2 is 2.44209228519 7305 7306Ei of 1.3 is 2.72139888023 7307 7308Ei of 1.4 is 3.00720746415 7309 7310Ei of 1.5 is 3.30128544913 7311 7312Ei of 1.6 is 3.60531994902 7313 7314Ei of 1.7 is 3.92096320135 7315 7316Ei of 1.8 is 4.24986755749 7317 7318Ei of 1.9 is 4.59371368695 7319 7320Ei of 2.0 is 4.954234356 7321 7322 7323for x := -0.1 step -0.1 until -2.0 do 7324 do!*one!*int!:function(!Ei,x); 7325 7326 7327Ei of - 0.1 is - 1.82292395842 7328 7329Ei of - 0.2 is - 1.22265054418 7330 7331Ei of - 0.3 is - 0.905676651676 7332 7333Ei of - 0.4 is - 0.702380118866 7334 7335Ei of - 0.5 is - 0.559773594776 7336 7337Ei of - 0.6 is - 0.454379503189 7338 7339Ei of - 0.7 is - 0.373768843234 7340 7341Ei of - 0.8 is - 0.310596578546 7342 7343Ei of - 0.9 is - 0.260183939326 7344 7345Ei of -1 is - 0.219383934396 7346 7347Ei of - 1.1 is - 0.185990904536 7348 7349Ei of - 1.2 is - 0.158408436851 7350 7351Ei of - 1.3 is - 0.135450957849 7352 7353Ei of - 1.4 is - 0.116219312571 7354 7355Ei of - 1.5 is - 0.100019582407 7356 7357Ei of - 1.6 is - 0.0863083336975 7358 7359Ei of - 1.7 is - 0.0746546444013 7360 7361Ei of - 1.8 is - 0.0647131293639 7362 7363Ei of - 1.9 is - 0.0562043781745 7364 7365Ei of - 2.0 is - 0.0489005107081 7366 7367 7368for x := 0.0 step 0.1 until 2.0 do 7369 do!*one!*int!:function(!Si,x); 7370 7371 7372Si of 0 is 0 7373 7374Si of 0.1 is 0.0999444611083 7375 7376Si of 0.2 is 0.199556088526 7377 7378Si of 0.3 is 0.298504043807 7379 7380Si of 0.4 is 0.396461464751 7381 7382Si of 0.5 is 0.493107418043 7383 7384Si of 0.6 is 0.588128809608 7385 7386Si of 0.7 is 0.681222239117 7387 7388Si of 0.8 is 0.772095785482 7389 7390Si of 0.9 is 0.860470710745 7391 7392Si of 1 is 0.946083070367 7393 7394Si of 1.1 is 1.02868521867 7395 7396Si of 1.2 is 1.10804719901 7397 7398Si of 1.3 is 1.18395800908 7399 7400Si of 1.4 is 1.25622673278 7401 7402Si of 1.5 is 1.32468353117 7403 7404Si of 1.6 is 1.38918048587 7405 7406Si of 1.7 is 1.44959228968 7407 7408Si of 1.8 is 1.50581678026 7409 7410Si of 1.9 is 1.55777531375 7411 7412Si of 2.0 is 1.6054129768 7413 7414 7415for x := -0.1 step -0.1 until -2.0 do 7416 do!*one!*int!:function(!Si,x); 7417 7418 7419Si of - 0.1 is - 0.0999444611083 7420 7421Si of - 0.2 is - 0.199556088526 7422 7423Si of - 0.3 is - 0.298504043807 7424 7425Si of - 0.4 is - 0.396461464751 7426 7427Si of - 0.5 is - 0.493107418043 7428 7429Si of - 0.6 is - 0.588128809608 7430 7431Si of - 0.7 is - 0.681222239117 7432 7433Si of - 0.8 is - 0.772095785482 7434 7435Si of - 0.9 is - 0.860470710745 7436 7437Si of -1 is - 0.946083070367 7438 7439Si of - 1.1 is - 1.02868521867 7440 7441Si of - 1.2 is - 1.10804719901 7442 7443Si of - 1.3 is - 1.18395800908 7444 7445Si of - 1.4 is - 1.25622673278 7446 7447Si of - 1.5 is - 1.32468353117 7448 7449Si of - 1.6 is - 1.38918048587 7450 7451Si of - 1.7 is - 1.44959228968 7452 7453Si of - 1.8 is - 1.50581678026 7454 7455Si of - 1.9 is - 1.55777531375 7456 7457Si of - 2.0 is - 1.6054129768 7458 7459 7460for x := 0.1 step 0.1 until 2.0 do 7461 do!*one!*int!:function(!Ci,x); 7462 7463 7464Ci of 0.1 is - 1.72786838666 7465 7466Ci of 0.2 is - 1.04220559567 7467 7468Ci of 0.3 is - 0.649172932971 7469 7470Ci of 0.4 is - 0.378809346425 7471 7472Ci of 0.5 is - 0.177784078807 7473 7474Ci of 0.6 is - 0.0222707069593 7475 7476Ci of 0.7 is 0.100514707009 7477 7478Ci of 0.8 is 0.198278615952 7479 7480Ci of 0.9 is 0.276067830468 7481 7482Ci of 1 is 0.337403922901 7483 7484Ci of 1.1 is 0.384873377425 7485 7486Ci of 1.2 is 0.420459182894 7487 7488Ci of 1.3 is 0.445738567529 7489 7490Ci of 1.4 is 0.462006585095 7491 7492Ci of 1.5 is 0.470356317195 7493 7494Ci of 1.6 is 0.471732516932 7495 7496Ci of 1.7 is 0.466968364177 7497 7498Ci of 1.8 is 0.456811129418 7499 7500Ci of 1.9 is 0.441940349682 7501 7502Ci of 2.0 is 0.422980828775 7503 7504 7505for x := -0.1 step -0.1 until -2.0 do 7506 do!*one!*int!:function(!Ci,x); 7507 7508 7509Ci of - 0.1 is 3.14159265359*i - 1.72786838666 7510 7511Ci of - 0.2 is 3.14159265359*i - 1.04220559567 7512 7513Ci of - 0.3 is 3.14159265359*i - 0.649172932971 7514 7515Ci of - 0.4 is 3.14159265359*i - 0.378809346425 7516 7517Ci of - 0.5 is 3.14159265359*i - 0.177784078807 7518 7519Ci of - 0.6 is 3.14159265359*i - 0.0222707069593 7520 7521Ci of - 0.7 is 3.14159265359*i + 0.100514707009 7522 7523Ci of - 0.8 is 3.14159265359*i + 0.198278615952 7524 7525Ci of - 0.9 is 3.14159265359*i + 0.276067830468 7526 7527Ci of -1 is 3.14159265359*i + 0.337403922901 7528 7529Ci of - 1.1 is 3.14159265359*i + 0.384873377425 7530 7531Ci of - 1.2 is 3.14159265359*i + 0.420459182894 7532 7533Ci of - 1.3 is 3.14159265359*i + 0.445738567529 7534 7535Ci of - 1.4 is 3.14159265359*i + 0.462006585095 7536 7537Ci of - 1.5 is 3.14159265359*i + 0.470356317195 7538 7539Ci of - 1.6 is 3.14159265359*i + 0.471732516932 7540 7541Ci of - 1.7 is 3.14159265359*i + 0.466968364177 7542 7543Ci of - 1.8 is 3.14159265359*i + 0.456811129418 7544 7545Ci of - 1.9 is 3.14159265359*i + 0.441940349682 7546 7547Ci of - 2.0 is 3.14159265359*i + 0.422980828775 7548 7549 7550for x := 0.0 step 0.1 until 2.0 do 7551 do!*one!*int!:function(!Shi,x); 7552 7553 7554Shi of 0 is 0 7555 7556Shi of 0.1 is 0.100055572225 7557 7558Shi of 0.2 is 0.200444978141 7559 7560Shi of 0.3 is 0.301504056205 7561 7562Shi of 0.4 is 0.403572668742 7563 7564Shi of 0.5 is 0.50699674982 7565 7566Shi of 0.6 is 0.612130396563 7567 7568Shi of 0.7 is 0.719338018929 7569 7570Shi of 0.8 is 0.828996563379 7571 7572Shi of 0.9 is 0.941497826511 7573 7574Shi of 1 is 1.05725087538 7575 7576Shi of 1.1 is 1.17668459205 7577 7578Shi of 1.2 is 1.30025036102 7579 7580Shi of 1.3 is 1.42842491904 7581 7582Shi of 1.4 is 1.56171338836 7583 7584Shi of 1.5 is 1.70065251577 7585 7586Shi of 1.6 is 1.84581414136 7587 7588Shi of 1.7 is 1.99780892288 7589 7590Shi of 1.8 is 2.15729034343 7591 7592Shi of 1.9 is 2.32495903256 7593 7594Shi of 2.0 is 2.50156743335 7595 7596 7597for x := -0.1 step -0.1 until -2.0 do 7598 do!*one!*int!:function(!Shi,x); 7599 7600 7601Shi of - 0.1 is - 0.100055572225 7602 7603Shi of - 0.2 is - 0.200444978141 7604 7605Shi of - 0.3 is - 0.301504056205 7606 7607Shi of - 0.4 is - 0.403572668742 7608 7609Shi of - 0.5 is - 0.50699674982 7610 7611Shi of - 0.6 is - 0.612130396563 7612 7613Shi of - 0.7 is - 0.719338018929 7614 7615Shi of - 0.8 is - 0.828996563379 7616 7617Shi of - 0.9 is - 0.941497826511 7618 7619Shi of -1 is - 1.05725087538 7620 7621Shi of - 1.1 is - 1.17668459205 7622 7623Shi of - 1.2 is - 1.30025036102 7624 7625Shi of - 1.3 is - 1.42842491904 7626 7627Shi of - 1.4 is - 1.56171338836 7628 7629Shi of - 1.5 is - 1.70065251577 7630 7631Shi of - 1.6 is - 1.84581414136 7632 7633Shi of - 1.7 is - 1.99780892288 7634 7635Shi of - 1.8 is - 2.15729034343 7636 7637Shi of - 1.9 is - 2.32495903256 7638 7639Shi of - 2.0 is - 2.50156743335 7640 7641 7642for x := 0.1 step 0.1 until 2.0 do 7643 do!*one!*int!:function(!Chi,x); 7644 7645 7646Chi of 0.1 is - 1.72286838619 7647 7648Chi of 0.2 is - 1.02220556604 7649 7650Chi of 0.3 is - 0.604172595471 7651 7652Chi of 0.4 is - 0.298807450123 7653 7654Chi of 0.5 is - 0.0527768449565 7655 7656Chi of 0.6 is 0.157750893374 7657 7658Chi of 0.7 is 0.345569175695 7659 7660Chi of 0.8 is 0.518399984833 7661 7662Chi of 0.9 is 0.681313887185 7663 7664Chi of 1 is 0.83786694098 7665 7666Chi of 1.1 is 0.990693687514 7667 7668Chi of 1.2 is 1.14184192417 7669 7670Chi of 1.3 is 1.29297396119 7671 7672Chi of 1.4 is 1.44549407579 7673 7674Chi of 1.5 is 1.60063293336 7675 7676Chi of 1.6 is 1.75950580766 7677 7678Chi of 1.7 is 1.92315427848 7679 7680Chi of 1.8 is 2.09257721406 7681 7682Chi of 1.9 is 2.26875465439 7683 7684Chi of 2.0 is 2.45266692265 7685 7686 7687for x := -0.1 step -0.1 until -2.0 do 7688 do!*one!*int!:function(!Chi,x); 7689 7690 7691Chi of - 0.1 is 3.14159265359*i - 1.72286838619 7692 7693Chi of - 0.2 is 3.14159265359*i - 1.02220556604 7694 7695Chi of - 0.3 is 3.14159265359*i - 0.604172595471 7696 7697Chi of - 0.4 is 3.14159265359*i - 0.298807450123 7698 7699Chi of - 0.5 is 3.14159265359*i - 0.0527768449565 7700 7701Chi of - 0.6 is 3.14159265359*i + 0.157750893374 7702 7703Chi of - 0.7 is 3.14159265359*i + 0.345569175695 7704 7705Chi of - 0.8 is 3.14159265359*i + 0.518399984833 7706 7707Chi of - 0.9 is 3.14159265359*i + 0.681313887185 7708 7709Chi of -1 is 3.14159265359*i + 0.83786694098 7710 7711Chi of - 1.1 is 3.14159265359*i + 0.990693687514 7712 7713Chi of - 1.2 is 3.14159265359*i + 1.14184192417 7714 7715Chi of - 1.3 is 3.14159265359*i + 1.29297396119 7716 7717Chi of - 1.4 is 3.14159265359*i + 1.44549407579 7718 7719Chi of - 1.5 is 3.14159265359*i + 1.60063293336 7720 7721Chi of - 1.6 is 3.14159265359*i + 1.75950580766 7722 7723Chi of - 1.7 is 3.14159265359*i + 1.92315427848 7724 7725Chi of - 1.8 is 3.14159265359*i + 2.09257721406 7726 7727Chi of - 1.9 is 3.14159265359*i + 2.26875465439 7728 7729Chi of - 2.0 is 3.14159265359*i + 2.45266692265 7730 7731 7732for x := 0.1 step 0.1 until 2.0 do 7733 do!*one!*int!:function(!Fresnel_!S,x); 7734 7735 7736Fresnel_S of 0.1 is 0.000523589547612 7737 7738Fresnel_S of 0.2 is 0.00418760916166 7739 7740Fresnel_S of 0.3 is 0.0141169980066 7741 7742Fresnel_S of 0.4 is 0.0333594326606 7743 7744Fresnel_S of 0.5 is 0.06473243286 7745 7746Fresnel_S of 0.6 is 0.110540207359 7747 7748Fresnel_S of 0.7 is 0.172136457863 7749 7750Fresnel_S of 0.8 is 0.249341393054 7751 7752Fresnel_S of 0.9 is 0.339776344393 7753 7754Fresnel_S of 1 is 0.43825914739 7755 7756Fresnel_S of 1.1 is 0.536497911097 7757 7758Fresnel_S of 1.2 is 0.623400918546 7759 7760Fresnel_S of 1.3 is 0.686333285535 7761 7762Fresnel_S of 1.4 is 0.713525077363 7763 7764Fresnel_S of 1.5 is 0.697504960082 7765 7766Fresnel_S of 1.6 is 0.638887683509 7767 7768Fresnel_S of 1.7 is 0.549195940322 7769 7770Fresnel_S of 1.8 is 0.450938769268 7771 7772Fresnel_S of 1.9 is 0.373347317817 7773 7774Fresnel_S of 2.0 is 0.343415678364 7775 7776 for x := -0.1 step -0.1 until -2.0 do 7777 do!*one!*int!:function(!Fresnel_!S,x); 7778 7779 7780Fresnel_S of - 0.1 is - 0.000523589547612 7781 7782Fresnel_S of - 0.2 is - 0.00418760916166 7783 7784Fresnel_S of - 0.3 is - 0.0141169980066 7785 7786Fresnel_S of - 0.4 is - 0.0333594326606 7787 7788Fresnel_S of - 0.5 is - 0.06473243286 7789 7790Fresnel_S of - 0.6 is - 0.110540207359 7791 7792Fresnel_S of - 0.7 is - 0.172136457863 7793 7794Fresnel_S of - 0.8 is - 0.249341393054 7795 7796Fresnel_S of - 0.9 is - 0.339776344393 7797 7798Fresnel_S of -1 is - 0.43825914739 7799 7800Fresnel_S of - 1.1 is - 0.536497911097 7801 7802Fresnel_S of - 1.2 is - 0.623400918546 7803 7804Fresnel_S of - 1.3 is - 0.686333285535 7805 7806Fresnel_S of - 1.4 is - 0.713525077363 7807 7808Fresnel_S of - 1.5 is - 0.697504960082 7809 7810Fresnel_S of - 1.6 is - 0.638887683509 7811 7812Fresnel_S of - 1.7 is - 0.549195940322 7813 7814Fresnel_S of - 1.8 is - 0.450938769268 7815 7816Fresnel_S of - 1.9 is - 0.373347317817 7817 7818Fresnel_S of - 2.0 is - 0.343415678364 7819 7820 7821for x := 0.1 step 0.1 until 2.0 do 7822 do!*one!*int!:function(!Fresnel_!C,x); 7823 7824 7825Fresnel_C of 0.1 is 0.0999975326271 7826 7827Fresnel_C of 0.2 is 0.199921057594 7828 7829Fresnel_C of 0.3 is 0.299400976052 7830 7831Fresnel_C of 0.4 is 0.397480759172 7832 7833Fresnel_C of 0.5 is 0.492344225871 7834 7835Fresnel_C of 0.6 is 0.581095446992 7836 7837Fresnel_C of 0.7 is 0.659652351905 7838 7839Fresnel_C of 0.8 is 0.722844171896 7840 7841Fresnel_C of 0.9 is 0.764823021273 7842 7843Fresnel_C of 1 is 0.779893400377 7844 7845Fresnel_C of 1.1 is 0.763806666062 7846 7847Fresnel_C of 1.2 is 0.715437722923 7848 7849Fresnel_C of 1.3 is 0.638550454727 7850 7851Fresnel_C of 1.4 is 0.543095783546 7852 7853Fresnel_C of 1.5 is 0.44526117604 7854 7855Fresnel_C of 1.6 is 0.36546168344 7856 7857Fresnel_C of 1.7 is 0.323826876004 7858 7859Fresnel_C of 1.8 is 0.333632927222 7860 7861Fresnel_C of 1.9 is 0.394470534892 7862 7863Fresnel_C of 2.0 is 0.488253406075 7864 7865 7866for x := -0.1 step -0.1 until -2.0 do 7867 do!*one!*int!:function(!Fresnel_!C,x); 7868 7869 7870Fresnel_C of - 0.1 is - 0.0999975326271 7871 7872Fresnel_C of - 0.2 is - 0.199921057594 7873 7874Fresnel_C of - 0.3 is - 0.299400976052 7875 7876Fresnel_C of - 0.4 is - 0.397480759172 7877 7878Fresnel_C of - 0.5 is - 0.492344225871 7879 7880Fresnel_C of - 0.6 is - 0.581095446992 7881 7882Fresnel_C of - 0.7 is - 0.659652351905 7883 7884Fresnel_C of - 0.8 is - 0.722844171896 7885 7886Fresnel_C of - 0.9 is - 0.764823021273 7887 7888Fresnel_C of -1 is - 0.779893400377 7889 7890Fresnel_C of - 1.1 is - 0.763806666062 7891 7892Fresnel_C of - 1.2 is - 0.715437722923 7893 7894Fresnel_C of - 1.3 is - 0.638550454727 7895 7896Fresnel_C of - 1.4 is - 0.543095783546 7897 7898Fresnel_C of - 1.5 is - 0.44526117604 7899 7900Fresnel_C of - 1.6 is - 0.36546168344 7901 7902Fresnel_C of - 1.7 is - 0.323826876004 7903 7904Fresnel_C of - 1.8 is - 0.333632927222 7905 7906Fresnel_C of - 1.9 is - 0.394470534892 7907 7908Fresnel_C of - 2.0 is - 0.488253406075 7909 7910 7911off rounded; 7912 7913 7914 7915% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 7916 7917% 12. Dilogarithm, polylogartihm and Lerch_phi 7918 7919% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 7920 7921 7922polylog(n,0); 7923 7924 79250 7926 7927 7928polylog(2,1); 7929 7930 7931 2 7932 pi 7933----- 7934 6 7935 7936 7937polylog(3,1); 7938 7939 7940zeta(3) 7941 7942 7943polylog(2,i); 7944 7945 7946 2 7947 48*catalan*i - pi 7948-------------------- 7949 48 7950 7951 7952df(polylog(a,x),x); 7953 7954 7955 - log( - x + 1) 7956------------------ 7957 x 7958 7959 7960polylog(1,x); 7961 7962 7963 - log( - x + 1) 7964 7965 7966precision reset; 7967 7968 796912 7970 7971on rounded; 7972 7973 7974 7975polylog(2,1/3); 7976 7977 79780.366213229977 7979 7980 7981off rounded; 7982 7983 7984 7985 7986Lerch_phi(3,4,1); 7987 7988 7989 polylog(4,3) 7990-------------- 7991 3 7992 7993 7994Lerch_phi(4,0,3); 7995 7996 7997 - 1 7998------ 7999 3 8000 8001 8002Lerch_phi(x,a,1); 8003 8004 8005 polylog(2,x) 8006-------------- 8007 x 8008 8009 8010Lerch_phi(1,x,1); 8011 8012 8013zeta(x) 8014 8015 8016df(Lerch_phi(x,3,4),x); 8017 8018 8019 - 4*lerch_phi(x,3,4) + lerch_phi(x,2,4) 8020------------------------------------------ 8021 x 8022 8023 8024 8025% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 8026 8027% 13. Constants 8028 8029% =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= 8030 8031on rounded; 8032 8033 8034off complex; 8035 8036 8037 8038precision 50; 8039 8040 804112 8042 8043 8044Euler_gamma; 8045 8046 80470.57721566490153286060651209008240243104215933593992 8048 8049 8050Khinchin; 8051 8052 80532.6854520010653064453097148354817956938203822939945 8054 8055 8056golden_ratio; 8057 8058 80591.6180339887498948482045868343656381177203091798058 8060 8061 8062Catalan; 8063 8064 80650.91596559417721901505460351493238411077414937428167 8066 8067 8068on complex; 8069 8070 8071*** Domain mode rounded changed to complex-rounded 8072 8073 8074Euler_gamma; 8075 8076 80770.57721566490153286060651209008240243104215933593992 8078 8079 8080Khinchin; 8081 8082 80832.6854520010653064453097148354817956938203822939945 8084 8085 8086golden_ratio; 8087 8088 80891.6180339887498948482045868343656381177203091798058 8090 8091 8092Catalan; 8093 8094 80950.91596559417721901505460351493238411077414937428167 8096 8097 8098 8099end; 8100