1/******************************************************************************* 2 3 Test file for the Exponential Integrals 4 5 by Dieter Kaiser (2008) 6*******************************************************************************/ 7 8kill(all); 9done; 10 11/* Define a test function for single values */ 12 13closeto(e,tol):=block([numer:true,abse],abse:abs(e),if(abse<tol) then true else abse); 14closeto(e,tol):=block([numer:true,abse],abse:abs(e),if(abse<tol) then true else abse); 15 16(test_value(actual, ref, digits) := closeto(realpart(actual)-realpart(ref), 10^(-digits)) and closeto(imagpart(actual)-imagpart(ref), 10^(-digits)), done); 17done; 18 19/******************************************************************************* 20 At first we check the special values of the Exponential Integrals 21*******************************************************************************/ 22 23errcatch(expintegral_e(0,0)); 24[]; 25errcatch(expintegral_e(0,0.0)); 26[]; 27errcatch(expintegral_e(0,0.0b0)); 28[]; 29 30errcatch(expintegral_ei(0)); 31[]; 32errcatch(expintegral_ei(0.0)); 33[]; 34errcatch(expintegral_ei(0.0b0)); 35[]; 36 37expintegral_li(0); 380; 39expintegral_li(0.0); 400.0; 41expintegral_li(0.0b0); 420.0b0; 43 44errcatch(expintegral_li(1)); 45[]; 46errcatch(expintegral_li(1.0)); 47[]; 48errcatch(expintegral_li(1.0b0)); 49[]; 50 51expintegral_si(0); 520; 53expintegral_si(0.0); 540.0; 55expintegral_si(0.0b0); 560.0b0; 57 58expintegral_shi(0); 590; 60expintegral_shi(0.0); 610.0; 62expintegral_shi(0.0b0); 630.0b0; 64 65errcatch(expintegral_ci(0)); 66[]; 67errcatch(expintegral_ci(0.0)); 68[]; 69errcatch(expintegral_ci(0.0b0)); 70[]; 71 72errcatch(expintegral_chi(0)); 73[]; 74errcatch(expintegral_chi(0.0)); 75[]; 76errcatch(expintegral_chi(0.0b0)); 77[]; 78 79/******************************************************************************* 80 Simplifications for the Exponential Integrals 81*******************************************************************************/ 82 83expintegral_e(-1,z); 84%e^(-z)*(z+1)/z^2; 85 86expintegral_e(-1,10); 8711*%e^-10/100; 88 89expintegral_e(-1,10+%i); 90(%i+11)*%e^(-%i-10)/(%i+10)^2; 91 92expintegral_e(0,z); 93%e^(-z)/z; 94 95expintegral_e(0,10); 96%e^-10/10; 97 98expintegral_e(0,10+%i); 99%e^(-10-%i)/(10+%i); 100 101/* The case Ev(0) simplifies to 1/(v-1) only for Re(v)>1 */ 102 103(assume(v>1), expintegral_e(v,0)); 1041/(v-1); 105 106expintegral_e(3/2+%i,0); 1071/(%i+1/2); 108 109errcatch(expintegral_e(1/2+%i,0)); 110[]; 111 112/* We don't simplify for infinities as an argument */ 113 114expintegral_e(-1,inf); 115expintegral_e(-1,inf); 116 117expintegral_e(v,infinity); 118expintegral_e(v,infinity); 119 120expintegral_e(minf,z); 121expintegral_e(minf,z); 122 123/* Realpart and imagpart for expintegral_e */ 124 125(assume(x_pos>0),done); 126done; 127 128/* a positive real value */ 129realpart(expintegral_e(v,x_pos)); 130expintegral_e(v,x_pos); 131imagpart(expintegral_e(v,x_pos)); 1320; 133 134/* a complex value */ 135realpart(expintegral_e(v,1+%i)); 1361/2*(expintegral_e(v,1-%i)+expintegral_e(v,1+%i)); 137imagpart(expintegral_e(v,1+%i)); 1381/2*%i*(expintegral_e(v,1-%i)-expintegral_e(v,1+%i)); 139 140/* Realpart and imagpart for expintegral_ei */ 141 142/* a real value */ 143realpart(expintegral_ei(x)); 144expintegral_ei(x); 145imagpart(expintegral_ei(x)); 1460; 147 148/* a complex value */ 149realpart(expintegral_ei(1+%i)); 1501/2*(expintegral_ei(1-%i)+expintegral_ei(1+%i)); 151imagpart(expintegral_ei(1+%i)); 1521/2*%i*(expintegral_ei(1-%i)-expintegral_ei(1+%i)); 153 154/* Realpart and imagpart for expintegral_si 155 expintegral_si has in addition reflection symmetry and 156 for a pure imaginary argument the result is pure imaginary */ 157 158/* a real value */ 159realpart(expintegral_si(x)); 160expintegral_si(x); 161imagpart(expintegral_si(x)); 1620; 163 164/* an imaginary value */ 165realpart(expintegral_si(%i)); 1660; 167imagpart(expintegral_si(%i)); 168-%i*expintegral_si(%i); 169 170/* a complex value */ 171realpart(expintegral_si(1+%i)); 1721/2*(expintegral_si(1-%i)+expintegral_si(1+%i)); 173imagpart(expintegral_si(1+%i)); 1741/2*%i*(expintegral_si(1-%i)-expintegral_si(1+%i)); 175 176/* Limits of expintegral_si */ 177 178limit(expintegral_si(x),x,inf); 179%pi/2; 180 181limit(expintegral_si(x),x,minf); 182-%pi/2; 183 184/* Limits of expintegral_shi */ 185 186limit(expintegral_shi(x),x,inf); 187inf; 188 189limit(expintegral_shi(x),x,minf); 190minf; 191 192/* Limits of expintegral_chi */ 193 194limit(expintegral_chi(x),x,inf); 195inf; 196 197limit(expintegral_chi(x),x,minf); 198inf; 199 200/******************************************************************************* 201 For a negative integer parameter we expand in a series 202*******************************************************************************/ 203 204expintegral_e(-5,z); 205120*(z^5/120+z^4/24+z^3/6+z^2/2+z+1)*%e^-z/z^6; 206 207/******************************************************************************* 208 For a half integral parameter we can expand in terms of the 209 Erfc or Erf function using the flag expintexpand. 210*******************************************************************************/ 211 212expintexpand:true; 213true; 214 215expintegral_e(1/2,z); 216sqrt(%pi)/sqrt(z)*erfc(sqrt(z)); 217 218expintegral_e(-1/2,z); 219sqrt(%pi)/(2*z^(3/2))*erfc(sqrt(z))+%e^(-z)/z; 220 221/* Expansion in terms of Erf for z = 1/2 222 We test the Expansion against a pure numerical evaluation. 223 The expansion works for complex argument too. 224 Attention: We have no support for Complex arguments of the Erf function. */ 225 226expintexpand:erf; 227erf; 228 229expintegral_e(5/2,1/2); 2302*sqrt(%pi)*(1-erf(1/sqrt(2)))/(3*sqrt(2)); 231 232/* We test the expansion against a pure numerical evaluation */ 233test_value(%,expintegral_e(2.5,0.5),15),numer; 234true; 235 236expintegral_e(-5/2,1/2); 237/* 2388*sqrt(2)*(15*sqrt(%pi)*(1-erf(1/sqrt(2)))/8+21/(4*sqrt(2)*sqrt(%e))); 239*/ 240 2412^(7/2)*(15*sqrt(%pi)*(1-erf(1/sqrt(2)))/8+(5/sqrt(2)+1/2^(5/2))/sqrt(%e)); 242 243test_value(%,expintegral_e(-2.5,0.5),13),numer; 244true; 245 246/******************************************************************************* 247 For a parameter which is a positive integer we can expand 248 the function in terms of the Exponential Integral Ei. 249*******************************************************************************/ 250 251expintegral_e(3,z); 252-z^2*(log(z)+(log(-1/z)-log(-z))/2+expintegral_ei(-z))/2-(z/2-1/2)*%e^-z; 253 254/* We compare this with numerical values */ 255 256ratsimp(expintegral_e(3,1/2)); 257(sqrt(%e)*(2*log(2)+log(-1/2)-2*expintegral_ei(-1/2)-log(-2))+4)/(16*sqrt(%e)); 258 259test_value(%,expintegral_e(3,0.5),15),numer; 260true; 261 262(expand:expintegral_e(10,1/2),done); 263done; 264 265test_value(expand,expintegral_e(10,0.5),15),numer; 266true; 267 268(expand:expintegral_e(100,1/2),done); 269done; 270 271test_value(expand,expintegral_e(100,0.5),15),numer; 272true; 273 274expintexpand:false; 275false; 276 277/******************************************************************************* 278 Do tests for additional float evaluation 279*******************************************************************************/ 280 281test_value( 282 expintegral_e(1,-1.700598-0.612828*%i), 283 1.229787425764198*%i-3.675726471068782,15); 284true; 285 286test_value( 287 expintegral_e(1,-1.5-%i*18.0), 288 0.181696882955049 + 0.16898654452488*%i,15); 289true; 290 291test_value( 292 expintegral_e(1,-1.5-%i*180.0), 293 .01998793885396577-.01484463667769751*%i,15); 294true; 295 296test_value( 297 expintegral_e(1,-15.0-%i*50.0), 298 62936.65453487506*%i-462.2396897671588,10); 299true; 300 301test_value( 302 expintegral_e(1,-15.0-%i*180.0), 303 15302.16784585461-9678.322938932864*%i,10); 304true; 305 306test_value( 307 expintegral_e(1,-150.0-%i*540.0), 308 2.479041623323267e+62*%i+2.105063890337474e+61,13-62); 309true; 310 311test_value( 312 expintegral_e(1,1.5+%i*18), 313 .01021327940204757-.006754558125326895*%i,15); 314true; 315 316test_value( 317 expintegral_e(1,15.0+%i*180.0), 318 1.129118870333903e-9*%i+1.261123517801268e-9,15); 319true; 320 321test_value( 322 expintegral_e(1,150.0+%i*540.0), 323 7.503677061484707e-69-1.036533879419174e-68*%i,15-69); 324true; 325 326 327 328 329 330/******************************************************************************* 331 Do tests for Bigfloat evaluation (values from functions.wolfram.com) 332*******************************************************************************/ 333 334/* Remember actual fpprec */ 335(oldfpprec:fpprec, fpprec:64, done); 336done; 337 338test_value( 339 expintegral_e(1,0.25b0), 340 1.044282634443738194536438161232282251891528374744802718635140468b0, 341 63); 342true; 343 344test_value( 345 expintegral_e(1,0.50b0), 346 0.5597735947761608117467959393150852352268468903163535152482932191b0, 347 63); 348true; 349 350test_value( 351 expintegral_e(1,1.50b0), 352 0.1000195824066326519019093399116669782617300061403505850505670604b0, 353 63); 354true; 355 356test_value( 357 expintegral_e(1,2.50b0), 358 0.02491491787026973549562801227460963594584838471142737701193454450b0, 359 64); 360true; 361 362test_value( 363 expintegral_e(1,0.5b0+%i), 364 - 0.0713947110424527235558849799368449390033695834555289289265924760b0 + 365 - 0.3574937736521626512548586934573247791553769710980144511429423771b0*%i, 366 62); 367true; 368 369test_value( 370 expintegral_ei(-0.5b0), 371 -0.5597735947761608117467959393150852352268468903163535152482932191b0, 372 63); 373true; 374 375test_value( 376 expintegral_ei(0.5b0), 377 0.4542199048631735799205238126628023652814055543526420451628177867b0, 378 63); 379true; 380 381test_value( 382 expintegral_ei(1.5b0), 383 3.301285449129797837957411316134742787656606985453422100762913970b0, 384 63); 385true; 386 387test_value( 388 expintegral_ei(1.5b0+%i), 389 2.799671509755731161198928033788660326920401659332834224954077897b0 + 390 2.737079221508684508327603325281307039723914975958035767630503279b0*%i, 391 63); 392true; 393 394test_value( 395 expintegral_li(-0.5b0), 396 0.058454819131659372625658464865614145649609292000300491927658936b0 + 397 3.265670174417890088883763125722547571780846521093778812746639381b0*%i, 398 63); 399true; 400 401test_value( 402 expintegral_li(0.5b0), 403 -0.3786710430610879767272071846365609805512340409782139969444209417b0, 404 63); 405true; 406 407test_value( 408 expintegral_li(1.5b0), 409 0.1250649863152963559943500047955129365420883239309922910956161087b0, 410 63); 411true; 412 413test_value( 414 expintegral_li(1.5b0+%i), 415 0.955549209862142878221358892328220253212569406502554250070344843b0 + 416 1.567751569664112401647194996566519972267813732803503976674771406b0*%i, 417 62); 418true; 419 420test_value( 421 expintegral_si(-0.5b0), 422 -0.4931074180430666891616267075727646536413371384287211316602426140b0, 423 63); 424true; 425 426test_value( 427 expintegral_si(0.5b0), 428 0.4931074180430666891616267075727646536413371384287211316602426140b0, 429 63); 430true; 431 432test_value( 433 expintegral_si(1.5b0), 434 1.324683531172119680370472846875214042814140454625112248480722201b0, 435 62.3b0); 436true; 437 438test_value( 439 expintegral_si(1.5b0+%i), 440 1.5324237219775529809013400344036774093828247429181012177841253510b0 + 441 0.6883092845662321107998443833405013522538814097236134325126725862b0*%i, 442 63); 443true; 444 445test_value( 446 expintegral_ci(-0.5b0), 447 -0.177784078806612901335810271070569078090519474812621968666825358b0 + 448 3.141592653589793238462643383279502884197169399375105820974944592b0*%i, 449 63); 450true; 451 452test_value( 453 expintegral_ci(0.5b0), 454 -0.1777840788066129013358102710705690780905194748126219686668253576b0, 455 63); 456true; 457 458test_value( 459 expintegral_ci(1.5b0), 460 0.4703563171953998866750821522365605516152327005730752953941674282b0, 461 62.2b0); 462true; 463 464test_value( 465 expintegral_ci(1.5b0+%i), 466 0.7839176551092182755417770543442248219437012644680041434724902541b0 - 467 0.0812194103150585766889706525256841552731980806778019973545925276b0*%i, 468 63); 469true; 470 471test_value( 472 expintegral_shi(-0.5b0), 473 -0.5069967498196671958336598759889438002541262223344977802055555029b0, 474 63); 475true; 476 477test_value( 478 expintegral_shi(0.5b0), 479 0.5069967498196671958336598759889438002541262223344977802055555029b0, 480 63); 481true; 482 483test_value( 484 expintegral_shi(1.5b0), 485 1.700652515768215244929660328023204882959168495796886342906740515b0, 486 63); 487true; 488 489test_value( 490 expintegral_shi(1.5b0+%i), 491 1.405456250564077987167827011345745730833834776665624179949753110b0 + 492 1.324296049597592107364382165946694647067190542728881672301521998b0*%i, 493 63); 494true; 495 496test_value( 497 expintegral_chi(-0.5b0), 498 -0.052776844956493615913136063326141434972720667981855735042737716b0 + 499 3.141592653589793238462643383279502884197169399375105820974944592b0*%i, 500 63); 501true; 502 503test_value( 504 expintegral_chi(0.5b0), 505 -0.05277684495649361591313606332614143497272066798185573504273771621b0, 506 63); 507true; 508 509test_value( 510 expintegral_chi(1.5b0), 511 1.600632933361582593027750988111537904697438489656535757856173455b0, 512 63); 513true; 514 515test_value( 516 expintegral_chi(1.5b0+%i), 517 1.394215259191653174031101022442914596086566882667210045004324787b0 + 518 1.412783171911092400963221159334612392656724433229154095328981281b0*%i, 519 63); 520true; 521 522 523/* restore fpprec */ 524(fpprec:oldfpprec, done); 525done; 526 527/******************************************************************************* 528 Do tests for additional big float evaluation 529*******************************************************************************/ 530 531/* Remember actual fpprec */ 532(oldfpprec:fpprec, fpprec:64, done); 533done; 534 535test_value( 536 expintegral_e(1,-1.5B0-%i*18.0B0), 537 1.689865445248795461022355866185975300284302677290211138169639712b-1*%i 538 +1.816968829550486868009237590887639256845378383882275967782801257b-1,63); 539true; 540 541test_value( 542 expintegral_e(1,-15.0B0-%i*50.0B0), 543 6.293665453487508854049428479450922789578087068032898765875144175b4*%i 544 -4.62239689767167158016168999268727094583699040537958778438547305b2,59); 545true; 546 547test_value( 548 expintegral_e(1,-1.5B0-%i*180.0B0), 549 1.998793885396577954161433015440646790143523658773070463290940391b-2 550 -1.48446366776975235341069111717359420933661819609933627048078479b-2*%i,64); 551true; 552 553test_value( 554 expintegral_e(1,-15.0B0-%i*180.0B0), 555 1.530216784585460659290957316900806622008438558612666623998533076b4 556 -9.678322938932862392009065659301165442754946683378713459319981218b3*%i,59); 557true; 558 559test_value( 560 expintegral_e(1,-150.0B0-%i*540.0B0), 561 2.47904162332326778788226522449358779416653162097669293288256403b62*%i 562 +2.105063890337477483794346786409993155624883726578689067616685218b61,1); 563true; 564 565test_value( 566 expintegral_e(1,1.5B0+%i*18.0B0), 567 1.021327940204755864240745590773899499558121729025330486880547885b-2 568 -6.754558125326884112691473105665013998699325818242672495399974279b-3*%i,65); 569true; 570 571test_value( 572 expintegral_e(1,15.0B0+%i*180.0B0), 573 1.129118870333903101943908390287222351537018836722867882019975027b-9*%i 574 +1.261123517801267593713906360450736314138456246082714062225342743b-9,72); 575true; 576 577test_value( 578 expintegral_e(1,150.0B0+%i*540.0B0), 579 7.50367706148470796758191535417179842322266910293477644515984948b-69 580 -1.03653387941917390868865781356557208741441722016128718318801276b-68*%i,-64-69); 581true; 582 583 584/* restore fpprec */ 585(fpprec:oldfpprec, done); 586done; 587 588/******************************************************************************* 589 Do tests for a parameter not an positive integer (double float arithmetic) 590*******************************************************************************/ 591 592test_value( 593 expintegral_e(0.5,0.5), 594 0.7953794908467029, 595 15); 596true; 597 598/* functions.wolfram.com get a small imaginary part. 599 Our algorithm gives a pure real result. That's correct. */ 600 601test_value( 602 expintegral_e(1.5,0.5), 603 0.4176818285785640 + 0.10d-16*%i, 604 15); 605true; 606 607test_value( 608 expintegral_e(1.5,1.5), 609 0.08475846798926254 + 0.10d-17*%i, 610 15); 611true; 612 613/* The algorithm works for an Complex parameter (not Bigfloat) too */ 614 615test_value( 616 expintegral_e(-0.25+%i,0.5), 617 0.7029675553348383 - 1.0854583859408265*%i, 618 15); 619true; 620 621test_value( 622 expintegral_e(0.5+%i,0.5), 623 0.5037890474837921 - 0.4713445822591324*%i, 624 15); 625true; 626 627test_value( 628 expintegral_e(0.5+%i,1.5), 629 0.10617497621984483 - 0.04370294969886679*%i, 630 15); 631true; 632 633/* For a negative integer as parameter the function will be expanded in a 634 finite series. We compare this result with the direct numerically 635 evaluation of the function. */ 636 637test_value(expintegral_e(-3,0.5)-expintegral_e(-3.0,0.5),0.0,13); 638true; 639 640/******************************************************************************* 641 Do tests for a parameter not an integer (Bigfloat arithmetic) 642*******************************************************************************/ 643 644/* Remember actual fpprec */ 645(oldfpprec:fpprec, fpprec:64, done); 646done; 647 648test_value( 649 expintegral_e(0.5,0.5b0), 650 0.7953794908467028960691560442509551305541581704269437959894550131b0, 651 61); 652true; 653 654/* functions.wolfram.com get a small imaginary part. 655 Our algorithm gives a pure real result. That's correct. */ 656 657test_value( 658 expintegral_e(1.5,0.5b0), 659 0.4176818285785639511384430257314057763296781005474301153763293043b0 + 660 0.10b-64*%i, 661 62); 662true; 663 664test_value( 665 expintegral_e(1.5,1.5b0), 666 0.08475846798926253566550159750486026149596073485977905694436004042b0 + 667 0.10b-65*%i, 668 63); 669true; 670 671/* restore fpprec */ 672(fpprec:oldfpprec, done); 673done; 674 675/******************************************************************************* 676 We check the transformation to another representation 677*******************************************************************************/ 678 679/* to prevent the simplification of 1/2*(log(z)-log(1/z))=0 which is wrong 680 for z a negative and real value we switch of logexpand */ 681 682(oldlogexpand:logexpand, logexpand:false); 683false; 684 685expintrep:gamma_incomplete; 686gamma_incomplete; 687 688expintegral_e(n,z); 689gamma_incomplete(1-n,z)*z^(n-1); 690 691expintegral_e(n,z); 692z^(n-1)*gamma_incomplete(1-n,z); 693 694expintegral_e1(z); 695gamma_incomplete(0,z); 696 697expintegral_ei(z); 698(log(z)-log(1/z))/2-log(-z)-gamma_incomplete(0,-z); 699 700expintegral_li(z); 701(log(log(z))-log(1/log(z)))/2-log(-log(z))-gamma_incomplete(0,-log(z)); 702 703expintegral_si(z); 704%i*(-log(%i*z)+log(-%i*z)-gamma_incomplete(0,%i*z)+gamma_incomplete(0,-%i*z))/2; 705 706expintegral_ci(z); 707log(z)-(log(%i*z)+log(-%i*z)+gamma_incomplete(0,%i*z)+gamma_incomplete(0,-%i*z))/2; 708 709expintegral_shi(z); 710(log(z)-log(-z)+gamma_incomplete(0,z)-gamma_incomplete(0,-z))/2; 711 712expintegral_chi(z); 713(-log(z)+log(-z)+gamma_incomplete(0,z)+gamma_incomplete(0,-z))/-2; 714 715expintrep:false; 716false; 717 718(logexpand:oldlogexpand,done); 719done; 720 721/* Do the functions have the appropriate symmetrie? 722 723 With the exception of exponential_ci we get for all tests a double float 724 zero or a Bigfloat zero. Because we use numercial evaluation this is not 725 natural and perhaps an effect only true with the GCL Compiler. 726 For the function expintegral_ci we get a small imaginary contribution which 727 is nearby zero. 728 729 Can this be verified by other Compilers? 730*/ 731 732z:0.5+%i; 7330.5+%i; 734 735expintegral_e(1,z) - conjugate(expintegral_e(1,conjugate(z))); 7360.0; 737 738expintegral_e(2,z) - conjugate(expintegral_e(2,conjugate(z))); 7390.0; 740 741expintegral_e(5,z) - conjugate(expintegral_e(5,conjugate(z))); 7420.0; 743 744expintegral_e(10,z) - conjugate(expintegral_e(10,conjugate(z))); 7450.0; 746 747expintegral_e1(z) - conjugate(expintegral_e1(conjugate(z))); 7480.0; 749 750expintegral_ei(z) - conjugate(expintegral_ei(conjugate(z))); 7510.0; 752 753expintegral_li(z) - conjugate(expintegral_li(conjugate(z))); 7540.0; 755 756expintegral_si(z) - conjugate(expintegral_si(conjugate(z))); 7570.0; 758 759test_value( 760 expintegral_ci(z) - conjugate(expintegral_ci(conjugate(z))), 761 0.0,15); 762true; 763 764expintegral_shi(z) - conjugate(expintegral_shi(conjugate(z))); 7650.0; 766 767expintegral_chi(z) - conjugate(expintegral_chi(conjugate(z))); 7680.0; 769 770/* The same for Bigfloats */ 771 772z:0.5b0+%i; 7730.5b0+%i; 774 775expintegral_e(1,z) - conjugate(expintegral_e(1,conjugate(z))); 7760.0b0; 777 778expintegral_e(2,z) - conjugate(expintegral_e(2,conjugate(z))); 7790.0b0; 780 781expintegral_e(5,z) - conjugate(expintegral_e(5,conjugate(z))); 7820.0b0; 783 784expintegral_e(10,z) - conjugate(expintegral_e(10,conjugate(z))); 7850.0b0; 786 787expintegral_e1(z) - conjugate(expintegral_e1(conjugate(z))); 7880.0b0; 789 790expintegral_ei(z) - conjugate(expintegral_ei(conjugate(z))); 7910.0b0; 792 793expintegral_li(z) - conjugate(expintegral_li(conjugate(z))); 7940.0b0; 795 796expintegral_si(z) - conjugate(expintegral_si(conjugate(z))); 7970.0b0; 798 799expintegral_ci(z) - conjugate(expintegral_ci(conjugate(z))); 8000.0b0; 801 802expintegral_shi(z) - conjugate(expintegral_shi(conjugate(z))); 8030.0b0; 804 805expintegral_chi(z) - conjugate(expintegral_chi(conjugate(z))); 8060.0b0; 807 808kill(z); 809done; 810 811/****************************************************************************** 812 813 Define test functions to do the tests with the numerical data 814 of the tables of A&S. 815 816 This routine is based on the algorithm to test the Wronskians in the 817 file rtest14.mac which was implemented by Raymond Toy. 818 819******************************************************************************/ 820 821(test_table(func,table,rows,eps) := 822block([badpoints : [], 823 abserr : 0, 824 maxerr : -1, 825 numer : true], 826 for i:1 thru rows step 1 do 827 ( 828 z : table[i,0], 829 result : rectform(func(z)), 830 answer : table[i,1], 831 abserr : abs(result-answer), 832 maxerr : max(maxerr,abserr), 833 if abserr > eps then 834 ( 835 badpoints : cons ([z,result,answer,abserr],badpoints) 836 ) 837 ), 838 if badpoints # [] then 839 cons(maxerr,badpoints) 840 else 841 badpoints 842),done); 843done; 844 845/* Test function for a table with Complex values */ 846 847(test_complex_table(func,table,rows,eps) := 848block([badpoints : [], 849 abserr : 0, 850 maxerr : -1, 851 numer : true], 852 for i:1 thru rows step 1 do 853 ( 854 z : table[i,0]+%i*table[i,1], 855 result : rectform(func(z)), 856 answer : (table[i,2]+%i*table[i,3]), 857 abserr : abs(result-answer), 858 maxerr : max(maxerr,abserr), 859 if abserr > eps then 860 ( 861 badpoints : cons ([z,result,answer,abserr],badpoints) 862 ) 863 ), 864 if badpoints # [] then 865 cons(maxerr,badpoints) 866 else 867 badpoints 868),done); 869done; 870 871/*****************************************************************************/ 872 873/* Values for E[-2](z), E[-3](z) and E[-4](z) */ 874 875block( 876em2 : make_array(flonum,5,2), 877fillarray(em2,[ 8780.0,0.0, /* the first entry isn't tested */ 8790.5,15.7697971525285, 8801.0,1.83939720585721 881]),done); 882done; 883 884block( 885em3 : make_array(flonum,5,2), 886fillarray(em3,[ 8870.0, 0.0, /* the first entry isn't tested */ 8880.5, 95.8318442345961, 8891.0, 5.88607105874308 890]),done); 891done; 892 893block( 894em4 : make_array(flonum,5,2), 895fillarray(em4,[ 8960.0, 0.0, /* the first entry isn't tested */ 8970.5, 767.8678151961939, 8981.0, 23.91216367614375 899]),done); 900done; 901 902/* Values for E2(z) from wolfram.functions.com */ 903 904block( 905e2 : make_array(flonum,20,4), 906fillarray(e2,[ 9070.0, 0.0, 0.0, 0.0, 9080.5, 0.0, 0.326643862324553, 0.0, 9091.0, 0.0, 0.148495506775922, 0.0, 9101.5, 0.0, 0.0731007865384809, 0.0, 911 912-1.5, 0.0, -0.47023910335663, -4.71238898038469, 913-1.0, 0.0, 0.82316401210311, -3.14159265358979, 914-0.5, 0.0, 1.42161131826854, -1.57079632679490, 915 9160.5, 1.0, 0.005913495891524, -0.260236353676039, 9171.0, 1.0, 0.0191599508550726, -0.1305169650657347, 9181.5, 1.0, 0.0152091306647864, -0.0662678635026173, 919 920-1.5, 1.0, -2.18255375782701, -1.57830995398609, 921-1.0, 1.0, -1.04975484772724, -1.27655210369426, 922-0.5, 1.0, -0.386354424417090, -0.872308287488887 923]),done); 924done; 925 926/* Do the tests with the above test data */ 927 928test_table(lambda([z],expintegral_e(-2,z)),'em2,2,3.5e-14); 929[]; 930 931test_table(lambda([z],expintegral_e(-3,z)),'em3,2,2.9e-14); 932[]; 933 934test_table(lambda([z],expintegral_e(-4,z)),'em4,2,1.0e-15); 935[]; 936 937test_complex_table(lambda([z],expintegral_e(2,z)),'e2,12,3.9e-15); 938[]; 939 940/***************************************************************************** 941 A&S Table 5.1 p. 238, values for Si(x)/x from 0.00 through 0.50 942******************************************************************************/ 943 944block( 945si_1 : make_array(flonum,51,2), 946fillarray(si_1,[ /* We start the loop for the test with i=1. */ 9470.00,1.0000000000, /* Therefore we don't do the the test for the first value */ 9480.01,0.9999944444, 9490.02,0.9999777781, 9500.03,0.9999500014, 9510.04,0.9999111154, 9520.05,0.9998611215, 9530.06,0.9998000216, 9540.07,0.9997278178, 9550.08,0.9996445127, 9560.09,0.9995501094, 9570.10,0.9994446111, 9580.11,0.9993280218, 9590.12,0.9992003455, 9600.13,0.9990615870, 9610.14,0.9989117512, 9620.15,0.9987508435, 9630.16,0.9985788696, 9640.17,0.9983958357, 9650.18,0.9982017486, 9660.19,0.9979966151, 9670.20,0.9977804427, 9680.21,0.9975532390, 9690.22,0.9973150122, 9700.23,0.9970657709, 9710.24,0.9968055242, 9720.25,0.9965342813, 9730.26,0.9962520519, 9740.27,0.9959588464, 9750.28,0.9956546750, 9760.29,0.9953395489, 9770.30,0.9950134793, 9780.31,0.9946764779, 9790.32,0.9943285570, 9800.33,0.9939697288, 9810.34,0.9936000064, 9820.35,0.9932194028, 983 9840.36,0.9928279320, 9850.37,0.9924256078, 9860.38,0.9920124449, 9870.39,0.9915884579, 9880.40,0.9911536619, 9890.41,0.9907080728, 9900.42,0.9902517063, 9910.43,0.9897845790, 9920.44,0.9893067074, 9930.45,0.9888181089, 9940.46,0.9883188008, 9950.47,0.9878088010, 9960.48,0.9872881278, 9970.49,0.9867567998, 9980.50,0.9862148361 999]),done); 1000done; 1001 1002test_table(lambda([z],expintegral_si(z)/z),'si_1,50,1.25e-10); 1003[]; 1004 1005/****************************************************************************** 1006 A&S Table 5.1 p. 239-243, values for Si(x) from 0.50 through 10.0 1007******************************************************************************/ 1008 1009block( 1010si_2 : make_array(flonum,231,2), 1011fillarray(si_2,[ 1012 10130.50,0.4931074180, 10140.51,0.5026877506, 10150.52,0.5122515212, 10160.53,0.5217984228, 10170.54,0.5313281492, 10180.55,0.5408403951, 10190.56,0.5503348563, 10200.57,0.5598112298, 10210.58,0.5692692137, 10220.59,0.5787085069, 10230.60,0.5881288096, 10240.61,0.5975298233, 10250.62,0.6069112503, 10260.63,0.6162727944, 10270.64,0.6256141603, 10280.65,0.6349350541, 10290.66,0.6442351831, 10300.67,0.6535142557, 10310.68,0.6627719817, 10320.69,0.6720080721, 10330.70,0.6812222391, 10340.71,0.6904141965, 10350.72,0.6995836590, 10360.73,0.7087303430, 10370.74,0.7178539660, 10380.75,0.7269542472, 10390.76,0.7360309067, 10400.77,0.7450836664, 10410.78,0.7541122494, 10420.79,0.7631163804, 10430.80,0.7720957855, 10440.81,0.7810501921, 10450.82,0.7899793293, 10460.83,0.7988829277, 10470.84,0.8077607191, 10480.85,0.8166124372, 10490.86,0.8254378170, 10500.87,0.8342365953, 10510.88,0.8430085102, 10520.89,0.8517533016, 10530.90,0.8604707107, 10540.91,0.8691604808, 10550.92,0.8778223564, 10560.93,0.8864560839, 10570.94,0.8950614112, 10580.95,0.9036380880, 10590.96,0.9121858656, 10600.97,0.9207044970, 10610.98,0.9291937370, 10620.99,0.9376533420, 1063 10641.00,0.9460830704, 10651.01,0.9544826820, 10661.02,0.9628519387, 10671.03,0.9711906039, 10681.04,0.9794984431, 10691.05,0.9877752233, 10701.06,0.9960207135, 10711.07,1.0042346846, 10721.08,1.0124169091, 10731.09,1.0205671617, 10741.10,1.0286852187, 10751.11,1.0367708583, 10761.12,1.0448238608, 10771.13,1.0528440082, 10781.14,1.0608310845, 10791.15,1.0687848757, 10801.16,1.0767051696, 10811.17,1.0845917561, 10821.18,1.0924444270, 10831.19,1.1002629760, 10841.20,1.1080471990, 10851.21,1.1157968937, 10861.22,1.1235118599, 10871.23,1.1311918994, 10881.24,1.1388368160, 10891.25,1.1464464157, 10901.26,1.1540205063, 10911.27,1.1615588978, 10921.28,1.1690614023, 10931.29,1.1765278340, 10941.30,1.1839580091, 10951.31,1.1913517459, 10961.32,1.1987088649, 10971.33,1.2060291886, 10981.34,1.2133125418, 10991.35,1.2205587513, 11001.36,1.2277676460, 11011.37,1.2349390571, 11021.38,1.2420728180, 11031.39,1.2491687640, 11041.40,1.2562267328, 11051.41,1.2632465642, 11061.42,1.2702281004, 11071.43,1.2771711854, 11081.44,1.2840756658, 11091.45,1.2909413902, 11101.46,1.2977682094, 11111.47,1.3045559767, 11121.48,1.3113045473, 11131.49,1.3180137788, 1114 11151.50,1.3246835312, 11161.51,1.3313136664, 11171.52,1.3379040489, 11181.53,1.3444545453, 11191.54,1.3509650245, 11201.55,1.3574353577, 11211.56,1.3638654183, 11221.57,1.3702550823, 11231.58,1.3766042276, 11241.59,1.3829127345, 11251.60,1.3891804859, 11261.61,1.3954073666, 11271.62,1.4015932640, 11281.63,1.4077380678, 11291.64,1.4138416698, 11301.65,1.4199039644, 11311.66,1.4259248482, 11321.67,1.4319042202, 11331.68,1.4378419816, 11341.69,1.4437380361, 11351.70,1.4495922897, 11361.71,1.4554046507, 11371.72,1.4611750299, 11381.73,1.4669033404, 11391.74,1.4725894974, 11401.75,1.4782334189, 11411.76,1.4838350249, 11421.77,1.4893942379, 11431.78,1.4949109830, 11441.79,1.5003851872, 11451.80,1.5058167803, 11461.81,1.5112056942, 11471.82,1.5165518633, 11481.83,1.5218552243, 11491.84,1.5271157165, 11501.85,1.5323332813, 11511.86,1.5375078626, 11521.87,1.5426394066, 11531.88,1.5477278621, 11541.89,1.5527731800, 11551.90,1.5577753137, 11561.91,1.5627342192, 11571.92,1.5676498545, 11581.93,1.5725221801, 11591.94,1.5773511591, 11601.95,1.5821367567, 11611.96,1.5868789407, 11621.97,1.5915776810, 11631.98,1.5962329502, 11641.99,1.6008447231, 1165 11662.0,1.6054129768, 11672.1,1.6486986362, 11682.2,1.6876248272, 11692.3,1.7222074818, 11702.4,1.7524855008, 11712.5,1.7785201734, 11722.6,1.8003944505, 11732.7,1.8182120765, 11742.8,1.8320965891, 11752.9,1.8421901946, 11763.0,1.8486525280, 11773.1,1.8516593077, 11783.2,1.8514008970, 11793.3,1.8480807828, 11803.4,1.8419139833, 11813.5,1.8331253987, 11823.6,1.8219481156, 11833.7,1.8086216809, 11843.8,1.7933903548, 11853.9,1.7765013604, 11864.0,1.7582031389, 11874.1,1.7387436265, 11884.2,1.7183685637, 11894.3,1.6973198507, 11904.4,1.6758339594, 11914.5,1.6541404144, 11924.6,1.6324603525, 11934.7,1.6110051718, 11944.8,1.5899752782, 11954.9,1.5695589381, 11965.0,1.5499312449, 11975.1,1.5312532047, 11985.2,1.5136709468, 11995.3,1.4973150636, 12005.4,1.4823000826, 12015.5,1.4687240727, 12025.6,1.4566683847, 12035.7,1.4461975285, 12045.8,1.4373591823, 12055.9,1.4301843341, 12066.0,1.4246875513, 12076.1,1.4208673734, 12086.2,1.4187068241, 12096.3,1.4181740348, 12106.4,1.4192229740, 12116.5,1.4217942744, 12126.6,1.4258161486, 12136.7,1.4312053853, 12146.8,1.4378684161, 12156.9,1.4457024427, 1216 12177.0,1.4545966142, 12187.1,1.4644332441, 12197.2,1.4750890554, 12207.3,1.4864364451, 12217.4,1.4983447533, 12227.5,1.5106815309, 12237.6,1.5233137914, 12247.7,1.5361092381, 12257.8,1.5489374581, 12267.9,1.5616710702, 12278.0,1.5741868217, 12288.1,1.5863666225, 12298.2,1.5980985106, 12308.3,1.6092775419, 12318.4,1.6198065968, 12328.5,1.6295970994, 12338.6,1.6385696454, 12348.7,1.6466545309, 12358.8,1.6537921861, 12368.9,1.6599335052, 12379.0,1.6650400758, 12389.1,1.6690843056, 12399.2,1.6720494480, 12409.3,1.6739295283, 12419.4,1.6747291725, 12429.5,1.6744633423, 12439.6,1.6731569803, 12449.7,1.6708445697, 12459.8,1.6675696169, 12469.9,1.6633840566, 124710.,1.6583475942 1248]),done); 1249done; 1250 1251test_table(lambda([z],expintegral_si(z)),'si_2,230,1.95e-10); 1252[]; 1253 1254/****************************************************************************** 1255 A&S Table 5.1 p. 238, values for (Ci(x)-log(x)-%gamma)/x 1256 from 0.00 through 0.50 1257******************************************************************************/ 1258 1259block( 1260ci_1 : make_array(flonum,55,2), 1261fillarray(ci_1,[ 12620.00,-0.2500000000, 12630.01,-0.2499989583, 12640.02,-0.2499958333, 12650.03,-0.2499906250, 12660.04,-0.2499833339, 12670.05,-0.2499739598, 12680.06,-0.2499625030, 12690.07,-0.2499489639, 12700.08,-0.2499333429, 12710.09,-0.2499156402, 12720.10,-0.2498958564, 12730.11,-0.2498739923, 12740.12,-0.2498500480, 12750.13,-0.2498240244, 12760.14,-0.2497959223, 12770.15,-0.2497657422, 12780.16,-0.2497334850, 12790.17,-0.2496991516, 12800.18,-0.2496627429, 12810.19,-0.2496242598, 12820.20,-0.2495837035, 12830.21,-0.2495410749, 12840.22,-0.2494963752, 12850.23,-0.2494496056, 12860.24,-0.2494007674, 12870.25,-0.2493498618, 12880.26,-0.2492968902, 12890.27,-0.2492418540, 12900.28,-0.2491847546, 12910.29,-0.2491255938, 12920.30,-0.2490643727, 12930.31,-0.2490010933, 12940.32,-0.2489357573, 12950.33,-0.2488683662, 12960.34,-0.2487989219, 12970.35,-0.2487274263, 12980.36,-0.2486538813, 12990.37,-0.2485782887, 13000.38,-0.2485006507, 13010.39,-0.2484209693, 13020.40,-0.2483392466, 13030.41,-0.2482554849, 13040.42,-0.2481696860, 13050.43,-0.2480818528, 13060.44,-0.2479919870, 13070.45,-0.2479000913, 13080.46,-0.2478061685, 13090.47,-0.2477102206, 13100.48,-0.2476122500, 13110.49,-0.2475122600, 13120.50,-0.2474102526]), done); 1313done; 1314 1315test_table( 1316 lambda([z],(expintegral_ci(z)-log(z)-%gamma)/z^2),'ci_1,50,1.95e-10); 1317[]; 1318 1319/****************************************************************************** 1320 A&S Table 5.1 p. 239-243, values for Ci(x) from 0.50 through 10.0 1321******************************************************************************/ 1322 1323block( 1324ci_2 : make_array(flonum,235,2), 1325fillarray(ci_2,[ 1326 13270.50,-0.1777840788, 13280.51,-0.1604532390, 13290.52,-0.1435537358, 13300.53,-0.1270707938, 13310.54,-0.1109904567, 13320.55,-0.0952995274, 13330.56,-0.0799855129, 13340.57,-0.0650365744, 13350.58,-0.0504414815, 13360.59,-0.0361895707, 13370.60,-0.0222707070, 13380.61,-0.0086752486, 13390.62,+0.0046059849, 13400.63,+0.0175817424, 13410.64,+0.0302603686, 13420.65,+0.0426498293, 13430.66,+0.0547577343, 13440.67,+0.0665913594, 13450.68,+0.0781576659, 13460.69,+0.0894633195, 13470.70,+0.1005147070, 13480.71,+0.1113179525, 13490.72,+0.1218789322, 13500.73,+0.1322032879, 13510.74,+0.1422964404, 13520.75,+0.1521636010, 13530.76,+0.1618097827, 13540.77,+0.1712398110, 13550.78,+0.1804583335, 13560.79,+0.1894698290, 13570.80,+0.1982786160, 13580.81,+0.2068888610, 13590.82,+0.2153045859, 13600.83,+0.2235296752, 13610.84,+0.2315678824, 13620.85,+0.2394228368, 13630.86,+0.2470980486, 13640.87,+0.2545969153, 13650.88,+0.2619227264, 13660.89,+0.2690786687, 13670.90,+0.2760678305, 13680.91,+0.2828932065, 13690.92,+0.2895577018, 13700.93,+0.2960641358, 13710.94,+0.3024152458, 13720.95,+0.3086136908, 13730.96,+0.3146620547, 13740.97,+0.3205628495, 13750.98,+0.3263185183, 13760.99,+0.3319314382, 1377 13781.00,0.3374039229, 13791.01,0.3427382254, 13801.02,0.3479365405, 13811.03,0.3530010067, 13821.04,0.3579337091, 13831.05,0.3627366810, 13841.06,0.3674119060, 13851.07,0.3719613201, 13861.08,0.3763868132, 13871.09,0.3806902312, 13881.10,0.3848733774, 13891.11,0.3889380142, 13901.12,0.3928858645, 13911.13,0.3967186134, 13921.14,0.4004379090, 13931.15,0.4040453647, 13941.16,0.4075425593, 13951.17,0.4109310390, 13961.18,0.4142123185, 13971.19,0.4173878816, 13981.20,0.4204591829, 13991.21,0.4234276482, 14001.22,0.4262946760, 14011.23,0.4290616379, 14021.24,0.4317298802, 14031.25,0.4343007240, 14041.26,0.4367754665, 14051.27,0.4391553815, 14061.28,0.4414417205, 14071.29,0.4436357130, 14081.30,0.4457385675, 14091.31,0.4477514723, 14101.32,0.4496755955, 14111.33,0.4515120863, 14121.34,0.4532620753, 14131.35,0.4549266752, 14141.36,0.4565069811, 14151.37,0.4580040711, 14161.38,0.4594190071, 14171.39,0.4607528349, 14181.40,0.4620065851, 14191.41,0.4631812730, 14201.42,0.4642778995, 14211.43,0.4652974513, 14221.44,0.4662409014, 14231.45,0.4671092094, 14241.46,0.4679033219, 14251.47,0.4686241732, 14261.48,0.4692726848, 14271.49,0.4698497667, 1428 14291.50,0.4703563172, 14301.51,0.4707932232, 14311.52,0.4711613608, 14321.53,0.4714615952, 14331.54,0.4716947815, 14341.55,0.4718617642, 14351.56,0.4719633785, 14361.57,0.4720004495, 14371.58,0.4719737932, 14381.59,0.4718842164, 14391.60,0.4717325169, 14401.61,0.4715194840, 14411.62,0.4712458984, 14421.63,0.4709125325, 14431.64,0.4705201507, 14441.65,0.4700695096, 14451.66,0.4695613580, 14461.67,0.4689964372, 14471.68,0.4683754812, 14481.69,0.4676992169, 14491.70,0.4669683642, 14501.71,0.4661836359, 14511.72,0.4653457385, 14521.73,0.4644553716, 14531.74,0.4635132286, 14541.75,0.4625199967, 14551.76,0.4614763568, 14561.77,0.4603829839, 14571.78,0.4592405471, 14581.79,0.4580497097, 14591.80,0.4568111294, 14601.81,0.4555254585, 14611.82,0.4541933436, 14621.83,0.4528154262, 14631.84,0.4513923427, 14641.85,0.4499247241, 14651.86,0.4484131966, 14661.87,0.4468583813, 14671.88,0.4452608948, 14681.89,0.4436213486, 14691.90,0.4419403497, 14701.91,0.4402185005, 14711.92,0.4384563991, 14721.93,0.4366546388, 14731.94,0.4348138088, 14741.95,0.4329344941, 14751.96,0.4310172752, 14761.97,0.4290627288, 14771.98,0.4270714273, 14781.99,0.4250439391, 1479 14802.0,+0.4229808288, 14812.1,+0.4005119878, 14822.2,+0.3750745990, 14832.3,+0.3471756175, 14842.4,+0.3172916174, 14852.5,+0.2858711964, 14862.6,+0.2533366161, 14872.7,+0.2200848786, 14882.8,+0.1864883896, 14892.9,+0.1528953242, 14903.0,+0.1196297860, 14913.1,+0.0869918312, 14923.2,+0.0552574117, 14933.3,+0.0246782846, 14943.4,-0.0045180779, 14953.5,-0.0321285485, 14963.6,-0.0579743519, 14973.7,-0.0819010013, 14983.8,-0.1037781504, 14993.9,-0.1234993492, 15004.0,-0.1409816979, 15014.1,-0.1561653918, 15024.2,-0.1690131568, 15034.3,-0.1795095725, 15044.4,-0.1876602868, 15054.5,-0.1934911221, 15064.6,-0.1970470797, 15074.7,-0.1983912468, 15084.8,-0.1976036133, 15094.9,-0.1947798060, 15105.0,-0.1900297497, 15115.1,-0.1834762632, 15125.2,-0.1752536023, 15135.3,-0.1655059586, 15145.4,-0.1543859262, 15155.5,-0.1420529476, 15165.6,-0.1286717494, 15175.7,-0.1144107808, 15185.8,-0.0994406647, 15195.9,-0.0839326741, 15206.0,-0.0680572439, 15216.1,-0.0519825290, 15226.2,-0.0358730193, 15236.3,-0.0198882206, 15246.4,-0.0041814110, 15256.5,+0.0111015195, 15266.6,+0.0258231381, 15276.7,+0.0398554400, 15286.8,+0.0530807167, 15296.9,+0.0653923140, 1530 15317.0,+0.0766952785, 15327.1,+0.0869068881, 15337.2,+0.0959570643, 15347.3,+0.1037886664, 15357.4,+0.1103576658, 15367.5,+0.1156332032, 15377.6,+0.1195975293, 15387.7,+0.1222458319, 15397.8,+0.1235859542, 15407.9,+0.1236380071, 15418.0,+0.1224338825, 15428.1,+0.1200166733, 15438.2,+0.1164400055, 15448.3,+0.1117672931, 15458.4,+0.1060709196, 15468.5,+0.0994313586, 15478.6,+0.0919362396, 15488.7,+0.0836793696, 15498.8,+0.0747597196, 15508.9,+0.0652803850, 15519.0,+0.0553475313, 15529.1,+0.0450693325, 15539.2,+0.0345549134, 15549.3,+0.0239133045, 15559.4,+0.0132524187, 15569.5,+0.0026780588, 15579.6,-0.0077070361, 15589.7,-0.0178040977, 15599.8,-0.0275191811, 15609.9,-0.0367639563, 156110.,-0.0454564330 1562]),done); 1563done; 1564 1565test_table(lambda([z],expintegral_ci(z)),'ci_2,230,3.2e-8); 1566[]; 1567 1568/****************************************************************************** 1569 A&S Table 5.1 p. 238, values for (Ei(x)-log(x)-%gamma)/x 1570 from 0.00 through 0.50 1571******************************************************************************/ 1572 1573block( 1574ei_1 : make_array(flonum,200,2), 1575fillarray(ei_1,[ 15760.00,1.000000000, 15770.01,1.002505566, 15780.02,1.005022306, 15790.03,1.007550283, 15800.04,1.010089560, 15810.05,1.012640202, 15820.06,1.015202272, 15830.07,1.017775836, 15840.08,1.020360958, 15850.09,1.022957705, 15860.10,1.025566141, 15870.11,1.028186335, 15880.12,1.030818352, 15890.13,1.033462259, 15900.14,1.036118125, 15910.15,1.038786018, 15920.16,1.041466006, 15930.17,1.044158158, 15940.18,1.046862544, 15950.19,1.049579234, 15960.20,1.052308298, 15970.21,1.055049807, 15980.22,1.057803833, 15990.23,1.060570446, 16000.24,1.063349719, 16010.25,1.066141726, 16020.26,1.068946539, 16030.27,1.071764232, 16040.28,1.074594879, 16050.29,1.077438555, 16060.30,1.080295334, 16070.31,1.083165293, 16080.32,1.086048507, 16090.33,1.088945053, 16100.34,1.091855008, 16110.35,1.094778451, 16120.36,1.097715458, 16130.37,1.100666108, 16140.38,1.103630481, 16150.39,1.106608656, 16160.40,1.109600714, 16170.41,1.112606735, 16180.42,1.115626800, 16190.43,1.118660991, 16200.44,1.121709391, 16210.45,1.124772082, 16220.46,1.127849147, 16230.47,1.130940671, 16240.48,1.134046738, 16250.49,1.137167432, 16260.50,1.140302841]),done); 1627done; 1628 1629test_table(lambda([z],(expintegral_ei(z)-log(z)-%gamma)/z),'ei_1,50,5.90e-10); 1630[]; 1631 1632/****************************************************************************** 1633 A&S Table 5.1 p. 239-241, values for Ei(x) from 0.50 through 2.00 1634******************************************************************************/ 1635 1636block( 1637ei_2 : make_array(flonum,235,2), 1638fillarray(ei_2,[ 1639 16400.50,0.454219905, 16410.51,0.487032167, 16420.52,0.519530633, 16430.53,0.551730445, 16440.54,0.583645931, 16450.55,0.615290657, 16460.56,0.646677490, 16470.57,0.677818642, 16480.58,0.708725720, 16490.59,0.739409764, 16500.60,0.769881290, 16510.61,0.800150320, 16520.62,0.830226417, 16530.63,0.860118716, 16540.64,0.889835949, 16550.65,0.919386468, 16560.66,0.948778277, 16570.67,0.978019042, 16580.68,1.007116121, 16590.69,1.036076576, 16600.70,1.064907195, 16610.71,1.093614501, 16620.72,1.122204777, 16630.73,1.150684069, 16640.74,1.179058208, 16650.75,1.207332816, 16660.76,1.235513319, 16670.77,1.263604960, 16680.78,1.291612805, 16690.79,1.319541753, 16700.80,1.347396548, 16710.81,1.375181783, 16720.82,1.402901910, 16730.83,1.430561245, 16740.84,1.458163978, 16750.85,1.485714176, 16760.86,1.513215791, 16770.87,1.540672664, 16780.88,1.568088534, 16790.89,1.595467036, 16800.90,1.622811714, 16810.91,1.650126019, 16820.92,1.677413317, 16830.93,1.704676891, 16840.94,1.731919946, 16850.95,1.759145612, 16860.96,1.786356947, 16870.97,1.813556941, 16880.98,1.840748519, 16890.99,1.867934543, 1690 16911.00,1.895117816, 16921.01,1.922301085, 16931.02,1.949487042, 16941.03,1.976678325, 16951.04,2.003877525, 16961.05,2.031087184, 16971.06,2.058309800, 16981.07,2.085547825, 16991.08,2.112803672, 17001.09,2.140079712, 17011.10,2.167378280, 17021.11,2.194701672, 17031.12,2.222052152, 17041.13,2.249431949, 17051.14,2.276843260, 17061.15,2.304288252, 17071.16,2.331769062, 17081.17,2.359287800, 17091.18,2.386846549, 17101.19,2.414447367, 17111.20,2.442092285, 17121.21,2.469783315, 17131.22,2.497522442, 17141.23,2.525311634, 17151.24,2.553152836, 17161.25,2.581047974, 17171.26,2.608998956, 17181.27,2.637007673, 17191.28,2.665075997, 17201.29,2.693205785, 17211.30,2.721398880, 17221.31,2.749657110, 17231.32,2.777982287, 17241.33,2.806376214, 17251.34,2.834840677, 17261.35,2.863377453, 17271.36,2.891988308, 17281.37,2.920674997, 17291.38,2.949439263, 17301.39,2.978282844, 17311.40,3.007207464, 17321.41,3.036214843, 17331.42,3.065306691, 17341.43,3.094484712, 17351.44,3.123750601, 17361.45,3.153106049, 17371.46,3.182552741, 17381.47,3.212092355, 17391.48,3.241726566, 17401.49,3.271457042, 1741 17421.50,3.301285449, 17431.51,3.331213449, 17441.52,3.361242701, 17451.53,3.391374858, 17461.54,3.421611576, 17471.55,3.451954503, 17481.56,3.482405289, 17491.57,3.512965580, 17501.58,3.543637024, 17511.59,3.574421266, 17521.60,3.605319949, 17531.61,3.636334719, 17541.62,3.667467221, 17551.63,3.698719099, 17561.64,3.730091999, 17571.65,3.761587569, 17581.66,3.793207456, 17591.67,3.824953310, 17601.68,3.856826782, 17611.69,3.888829528, 17621.70,3.920963201, 17631.71,3.953229462, 17641.72,3.985629972, 17651.73,4.018166395, 17661.74,4.050840400, 17671.75,4.083653659, 17681.76,4.116607847, 17691.77,4.149704645, 17701.78,4.182945736, 17711.79,4.216332809, 17721.80,4.249867557, 17731.81,4.283551681, 17741.82,4.317386883, 17751.83,4.351374872, 17761.84,4.385517364, 17771.85,4.419816080, 17781.86,4.454272746, 17791.87,4.488889097, 17801.88,4.523666872, 17811.89,4.558607817, 17821.90,4.593713687, 17831.91,4.628986242, 17841.92,4.664427249, 17851.93,4.700038485, 17861.94,4.735821734, 17871.95,4.771778785, 17881.96,4.807911438, 17891.97,4.844221501, 17901.98,4.880710791, 17911.99,4.917381131, 17922.00,4.954234356 1793]),done); 1794done; 1795 1796test_table(lambda([z],expintegral_ei(z)),'ei_2,150,5.70e-10); 1797[]; 1798 1799/****************************************************************************** 1800 A&S Table 5.1 p. 242-243, values for x*%e^(-x)*Ei(x) from 2.00 through 10.0 1801******************************************************************************/ 1802 1803block( 1804ei_3 : make_array(flonum,235,2), 1805fillarray(ei_3,[ 1806 18072.0,1.340965420, 18082.1,1.371486802, 18092.2,1.397421992, 18102.3,1.419171534, 18112.4,1.437118315, 18122.5,1.451625159, 18132.6,1.463033397, 18142.7,1.471662153, 18152.8,1.477808187, 18162.9,1.481746162, 18173.0,1.483729204, 18183.1,1.483989691, 18193.2,1.482740191, 18203.3,1.480174491, 18213.4,1.476468706, 18223.5,1.471782389, 18233.6,1.466259659, 18243.7,1.460030313, 18253.8,1.453210902, 18263.9,1.445905765, 18274.0,1.438208032, 18284.1,1.430200557, 18294.2,1.421956813, 18304.3,1.413541719, 18314.4,1.405012424, 18324.5,1.396419030, 18334.6,1.387805263, 18344.7,1.379209093, 18354.8,1.370663313, 18364.9,1.362196054, 18375.0,1.353831278, 18385.1,1.345589212, 18395.2,1.337486755, 18405.3,1.329537845, 18415.4,1.321753788, 18425.5,1.314143566, 18435.6,1.306714107, 18445.7,1.299470536, 18455.8,1.292416395, 18465.9,1.285553849, 18476.0,1.278883860, 18486.1,1.272406357, 18496.2,1.266120373, 18506.3,1.260024184, 18516.4,1.254115417, 18526.5,1.248391155, 18536.6,1.242848032, 18546.7,1.237482309, 18556.8,1.232289952, 18566.9,1.227266684, 18577.0,1.222408053, 18587.1,1.217709472, 18597.2,1.213166264, 18607.3,1.208773699, 18617.4,1.204527026, 18627.5,1.200421500, 18637.6,1.196452401, 18647.7,1.192615063, 18657.8,1.188904881, 18667.9,1.185317334, 18678.0,1.181847987, 18688.1,1.178492509, 18698.2,1.175246676, 18708.3,1.172106376, 18718.4,1.169067617, 18728.5,1.166126526, 18738.6,1.163279354, 18748.7,1.160522476, 18758.8,1.157852390, 18768.9,1.155265719, 18779.0,1.152759209, 18789.1,1.150329724, 18799.2,1.147974251, 18809.3,1.145689889, 18819.4,1.143473855, 18829.5,1.141323476, 18839.6,1.139236185, 18849.7,1.137209523, 18859.8,1.135241130, 18869.9,1.133328746, 188710.,1.131470205 1888]),done); 1889done; 1890 1891test_table(lambda([z],z*%e^(-z)*expintegral_ei(z)),'ei_3,80,8.95e-10); 1892[]; 1893 1894/****************************************************************************** 1895 A&S Table 5.1 p. 238, values for (E1(x)-log(x)-%gamma)/x 1896 from 0.00 through 0.50 1897******************************************************************************/ 1898 1899block( 1900e1_1 : make_array(flonum,200,2), 1901fillarray(e1_1,[ 1902 19030.00,1.0000000000, 19040.01,0.9975055452, 19050.02,0.9950221392, 19060.03,0.9925497201, 19070.04,0.9900882265, 19080.05,0.9876375971, 19090.06,0.9851977714, 19100.07,0.9827686889, 19110.08,0.9803502898, 19120.09,0.9779425142, 19130.10,0.9755453033, 19140.11,0.9731585980, 19150.12,0.9707823399, 19160.13,0.9684164710, 19170.14,0.9660609336, 19180.15,0.9637156702, 19190.16,0.9613806240, 19200.17,0.9590557383, 19210.18,0.9567409569, 19220.19,0.9544362237, 19230.20,0.9521414833, 19240.21,0.9498566804, 19250.22,0.9475817603, 19260.23,0.9453166684, 19270.24,0.9430613506, 19280.25,0.9408157528, 19290.26,0.9385798221, 19300.27,0.9363535046, 19310.28,0.9341367481, 19320.29,0.9319294997, 19330.30,0.9297317075, 19340.31,0.9275433196, 19350.32,0.9253642845, 19360.33,0.9231945510, 19370.34,0.9210340684, 19380.35,0.9188827858, 19390.36,0.9167406533, 19400.37,0.9146076209, 19410.38,0.9124836388, 19420.39,0.9103686582, 19430.40,0.9082626297, 19440.41,0.9061655048, 19450.42,0.9040772350, 19460.43,0.9019977725, 19470.44,0.8999270693, 19480.45,0.8978650778, 19490.46,0.8958117511, 19500.47,0.8937670423, 19510.48,0.8917309048, 19520.49,0.8897032920, 19530.50,0.8876841584 1954]),done); 1955done; 1956 1957test_table(lambda([z],(expintegral_e1(z)+log(z)+%gamma)/z),'e1_1,50,1.65e-10); 1958[]; 1959 1960/****************************************************************************** 1961 A&S Table 5.1 p. 239-241, values for E1(x) from 0.50 through 2.00 1962******************************************************************************/ 1963 1964block( 1965e1_2 : make_array(flonum,200,2), 1966fillarray(e1_2,[ 1967 19680.50,0.559773595, 19690.51,0.547822352, 19700.52,0.536219798, 19710.53,0.524951510, 19720.54,0.514003886, 19730.55,0.503364081, 19740.56,0.493019959, 19750.57,0.482960034, 19760.58,0.473173433, 19770.59,0.463649849, 19780.60,0.454379503, 19790.61,0.445353112, 19800.62,0.436561854, 19810.63,0.427997338, 19820.64,0.419651581, 19830.65,0.411516976, 19840.66,0.403586275, 19850.67,0.395852563, 19860.68,0.388309243, 19870.69,0.380950010, 19880.70,0.373768843, 19890.71,0.366759981, 19900.72,0.359917914, 19910.73,0.353237364, 19920.74,0.346713279, 19930.75,0.340340813, 19940.76,0.334115321, 19950.77,0.328032346, 19960.78,0.322087610, 19970.79,0.316277004, 19980.80,0.310596579, 19990.81,0.305042539, 20000.82,0.299611236, 20010.83,0.294299155, 20020.84,0.289102918, 20030.85,0.284019269, 20040.86,0.279045070, 20050.87,0.274177301, 20060.88,0.269413046, 20070.89,0.264749496, 20080.90,0.260183939, 20090.91,0.255713758, 20100.92,0.251336425, 20110.93,0.247049501, 20120.94,0.242850627, 20130.95,0.238737524, 20140.96,0.234707988, 20150.97,0.230759890, 20160.98,0.226891167, 20170.99,0.223099826, 2018 20191.00,0.219383934, 20201.01,0.215741624, 20211.02,0.212171083, 20221.03,0.208670559, 20231.04,0.205238352, 20241.05,0.201872813, 20251.06,0.198572347, 20261.07,0.195335403, 20271.08,0.192160479, 20281.09,0.189046118, 20291.10,0.185990905, 20301.11,0.182993465, 20311.12,0.180052467, 20321.13,0.177166615, 20331.14,0.174334651, 20341.15,0.171555354, 20351.16,0.168827535, 20361.17,0.166150040, 20371.18,0.163521748, 20381.19,0.160941567, 20391.20,0.158408437, 20401.21,0.155921324, 20411.22,0.153479226, 20421.23,0.151081164, 20431.24,0.148726188, 20441.25,0.146413373, 20451.26,0.144141815, 20461.27,0.141910639, 20471.28,0.139718989, 20481.29,0.137566032, 20491.30,0.135450958, 20501.31,0.133372975, 20511.32,0.131331314, 20521.33,0.129325224, 20531.34,0.127353972, 20541.35,0.125416844, 20551.36,0.123513146, 20561.37,0.121642198, 20571.38,0.119803337, 20581.39,0.117995919, 20591.40,0.116219313, 20601.41,0.114472903, 20611.42,0.112756090, 20621.43,0.111068287, 20631.44,0.109408923, 20641.45,0.107777440, 20651.46,0.106173291, 20661.47,0.104595946, 20671.48,0.103044882, 20681.49,0.101519593, 2069 20701.50,0.100019582, 20711.51,0.098544365, 20721.52,0.097093466, 20731.53,0.095666424, 20741.54,0.094262786, 20751.55,0.092882108, 20761.56,0.091523960, 20771.57,0.090187917, 20781.58,0.088873566, 20791.59,0.087580504, 20801.60,0.086308334, 20811.61,0.085056670, 20821.62,0.083825133, 20831.63,0.082613354, 20841.64,0.081420970, 20851.65,0.080247627, 20861.66,0.079092978, 20871.67,0.077956684, 20881.68,0.076838412, 20891.69,0.075737839, 20901.70,0.074654644, 20911.71,0.073588518, 20921.72,0.072539154, 20931.73,0.071506255, 20941.74,0.070489527, 20951.75,0.069488685, 20961.76,0.068503447, 20971.77,0.067533539, 20981.78,0.066578691, 20991.79,0.065638641, 21001.80,0.064713129, 21011.81,0.063801903, 21021.82,0.062904715, 21031.83,0.062021320, 21041.84,0.061151482, 21051.85,0.060294967, 21061.86,0.059451545, 21071.87,0.058620994, 21081.88,0.057803091, 21091.89,0.056997623, 21101.90,0.056204378, 21111.91,0.055423149, 21121.92,0.054653731, 21131.93,0.053895927, 21141.94,0.053149540, 21151.95,0.052414380, 21161.96,0.051690257, 21171.97,0.050976988, 21181.98,0.050274392, 21191.99,0.049582291, 21202.00,0.048900511 2121]),done); 2122done; 2123 2124test_table(lambda([z],expintegral_e1(z)),'e1_2,150,5.35e-10); 2125[]; 2126 2127/****************************************************************************** 2128 A&S Table 5.1 p. 242-243, values for x*%e^x*E1(x) from 2.00 through 10.0 2129******************************************************************************/ 2130 2131block( 2132e1_3 : make_array(flonum,200,2), 2133fillarray(e1_3,[ 2134 21352.0,0.722657234, 21362.1,0.730791502, 21372.2,0.738431132, 21382.3,0.745622149, 21392.4,0.752404829, 21402.5,0.758814592, 21412.6,0.764882722, 21422.7,0.770636987, 21432.8,0.776102123, 21442.9,0.781300252, 21453.0,0.786251221, 21463.1,0.790972900, 21473.2,0.795481422, 21483.3,0.799791408, 21493.4,0.803916127, 21503.5,0.807867661, 21513.6,0.811657037, 21523.7,0.815294342, 21533.8,0.818788821, 21543.9,0.822148967, 21554.0,0.825382600, 21564.1,0.828496926, 21574.2,0.831498602, 21584.3,0.834393794, 21594.4,0.837188207, 21604.5,0.839887144, 21614.6,0.842495539, 21624.7,0.845017971, 21634.8,0.847458721, 21644.9,0.849821778, 21655.0,0.852110880, 21665.1,0.854329519, 21675.2,0.856480958, 21685.3,0.858568275, 21695.4,0.860594348, 21705.5,0.862561885, 21715.6,0.864473436, 21725.7,0.866331399, 21735.8,0.868138040, 21745.9,0.869895494, 21756.0,0.871605775, 21766.1,0.873270793, 21776.2,0.874892347, 21786.3,0.876472150, 21796.4,0.878011816, 21806.5,0.879512881, 21816.6,0.880976797, 21826.7,0.882404955, 21836.8,0.883798662, 21846.9,0.885159176, 21857.0,0.886487675, 21867.1,0.887785294, 21877.2,0.889053119, 21887.3,0.890292173, 21897.4,0.891503440, 21907.5,0.892687854, 21917.6,0.893846312, 21927.7,0.894979666, 21937.8,0.896088737, 21947.9,0.897174302, 21958.0,0.898237113, 21968.1,0.899277888, 21978.2,0.900297306, 21988.3,0.901296033, 21998.4,0.902274699, 22008.5,0.903233900, 22018.6,0.904174228, 22028.7,0.905096235, 22038.8,0.906000459, 22048.9,0.906887415, 22059.0,0.907757602, 22069.1,0.908611483, 22079.2,0.909449530, 22089.3,0.910272177, 22099.4,0.911079850, 22109.5,0.911872958, 22119.6,0.912651897, 22129.7,0.913417043, 22139.8,0.914168766, 22149.9,0.914907418, 221510.,0.915633339 2216]),done); 2217done; 2218 2219test_table(lambda([z],z*%e^z*expintegral_e1(z)),'e1_3,80,2.50e-8); 2220[]; 2221 2222/****************************************************************************** 2223 A&S Table 5.6 p. 249-251, values for z*%e^z*E1(z) for Complex values 2224 from -19 through 20 for the Real part and 2225 from 0 through 20 for the Complex part 2226******************************************************************************/ 2227 2228block( 2229ec_1 : make_array(flonum,855,4), 2230fillarray(ec_1,[ 2231 2232/* Table 5.6 p. 249 */ 2233 2234-19,00,1.059305,0.000000, 2235-18,00,1.063087,0.000001, 2236-17,00,1.067394,0.000002, 2237-16,00,1.072345,0.000006, 2238-15,00,1.078103,0.000014, 2239 2240-19,01,1.059090,0.003539, 2241-18,01,1.062827,0.004010, 2242-17,01,1.067073,0.004584, 2243-16,01,1.071942,0.005296, 2244-15,01,1.077584,0.006195, 2245 2246-19,02,1.058456,0.007000, 2247-18,02,1.062061,0.007918, 2248-17,02,1.066135,0.009032, 2249-16,02,1.070774,0.010403, 2250-15,02,1.076102,0.012118, 2251 2252-19,03,1.057431,0.010310, 2253-18,03,1.060829,0.011633, 2254-17,03,1.064636,0.013226, 2255-16,03,1.068925,0.015172, 2256-15,03,1.073783,0.017579, 2257 2258-19,04,1.056058,0.013410, 2259-18,04,1.059190,0.015079, 2260-17,04,1.062657,0.017075, 2261-16,04,1.066508,0.019486, 2262-15,04,1.070793,0.022432, 2263 2264-19,05,1.054391,0.016252, 2265-18,05,1.057215,0.018202, 2266-17,05,1.060297,0.020512, 2267-16,05,1.063659,0.023272, 2268-15,05,1.067318,0.026598, 2269 2270-19,06,1.052490,0.018806, 2271-18,06,1.054981,0.020969, 2272-17,06,1.057655,0.023505, 2273-16,06,1.060510,0.026499, 2274-15,06,1.063538,0.030055, 2275 2276-19,07,1.050413,0.021055, 2277-18,07,1.052565,0.023364, 2278-17,07,1.054829,0.026044, 2279-16,07,1.057187,0.029167, 2280-15,07,1.059610,0.032823, 2281 2282-19,08,1.048217,0.022996, 2283-18,08,1.050037,0.025391, 2284-17,08,1.051905,0.028141, 2285-16,08,1.053795,0.031306, 2286-15,08,1.055664,0.034957, 2287 2288-19,09,1.045956,0.024637, 2289-18,09,1.047458,0.027066, 2290-17,09,1.048958,0.029824, 2291-16,09,1.050421,0.032960, 2292-15,09,1.051797,0.036527, 2293 2294-19,10,1.043672,0.025993, 2295-18,10,1.044880,0.028412, 2296-17,10,1.046045,0.031130, 2297-16,10,1.047129,0.034183, 2298-15,10,1.048081,0.037609, 2299 2300-19,11,1.041402,0.027086, 2301-18,11,1.042345,0.029461, 2302-17,11,1.043212,0.032102, 2303-16,11,1.043967,0.035034, 2304-15,11,1.044559,0.038282, 2305 2306-19,12,1.039177,0.027940, 2307-18,12,1.039882,0.030245, 2308-17,12,1.040490,0.032781, 2309-16,12,1.040965,0.035567, 2310-15,12,1.041259,0.038616, 2311 2312-19,13,1.037018,0.028581, 2313-18,13,1.037515,0.030796, 2314-17,13,1.037901,0.033211, 2315-16,13,1.038140,0.035836, 2316-15,13,1.038192,0.038677, 2317 2318-19,14,1.034942,0.029034, 2319-18,14,1.035259,0.031148, 2320-17,14,1.035456,0.033431, 2321-16,14,1.035501,0.035888, 2322-15,14,1.035359,0.038520, 2323 2324-19,15,1.032959,0.029326, 2325-18,15,1.033123,0.031330, 2326-17,15,1.033162,0.033476, 2327-16,15,1.033049,0.035765, 2328-15,15,1.032754,0.038193, 2329 2330-19,16,1.031076,0.029477, 2331-18,16,1.031110,0.031368, 2332-17,16,1.031019,0.033377, 2333-16,16,1.030780,0.035502, 2334-15,16,1.030365,0.037735, 2335 2336-19,17,1.029296,0.029511, 2337-18,17,1.029222,0.031288, 2338-17,17,1.029025,0.033162, 2339-16,17,1.028685,0.035129, 2340-15,17,1.028180,0.037179, 2341 2342-19,18,1.027620,0.029445, 2343-18,18,1.027456,0.031110, 2344-17,18,1.027174,0.032855, 2345-16,18,1.026756,0.034672, 2346-15,18,1.026183,0.036552, 2347 2348-19,19,1.026046,0.029296, 2349-18,19,1.025809,0.030854, 2350-17,19,1.025459,0.032474, 2351-16,19,1.024981,0.034150, 2352-15,19,1.024360,0.035873, 2353 2354-19,20,1.024570,0.029080, 2355-18,20,1.024275,0.030534, 2356-17,20,1.023872,0.032037, 2357-16,20,1.023349,0.033582, 2358-15,20,1.022695,0.035160, 2359 2360-14,00,1.084892,0.000037, 2361-13,00,1.093027,0.000092, 2362-12,00,1.102975,0.000232, 2363-11,00,1.115431,0.000577, 2364-10,00,1.131470,0.001426, 2365 2366-14,01,1.084200,0.007359, 2367-13,01,1.092067,0.008913, 2368-12,01,1.101566,0.011063, 2369-11,01,1.113230,0.014169, 2370-10,01,1.127796,0.018879, 2371 2372-14,02,1.082276,0.014306, 2373-13,02,1.089498,0.017161, 2374-12,02,1.098025,0.020981, 2375-11,02,1.108170,0.026241, 2376-10,02,1.120286,0.033700, 2377 2378-14,03,1.079313,0.020604, 2379-13,03,1.085635,0.024471, 2380-12,03,1.092873,0.029507, 2381-11,03,1.101137,0.036189, 2382-10,03,1.110462,0.045218, 2383 2384-14,04,1.075560,0.026075, 2385-13,04,1.080853,0.030637, 2386-12,04,1.086686,0.036422, 2387-11,04,1.093013,0.043843, 2388-10,04,1.099666,0.053451, 2389 2390-14,05,1.071279,0.030642, 2391-13,05,1.075522,0.035599, 2392-12,05,1.079985,0.041724, 2393-11,05,1.084526,0.049336, 2394-10,05,1.088877,0.058817, 2395 2396-14,06,1.066708,0.034303, 2397-13,06,1.069960,0.039405, 2398-12,06,1.073185,0.045552, 2399-11,06,1.076197,0.052967, 2400-10,06,1.078701,0.061886, 2401 2402-14,07,1.062046,0.037117, 2403-13,07,1.064412,0.042169, 2404-12,07,1.066578,0.048115, 2405-11,07,1.068350,0.055093, 2406-10,07,1.069450,0.063225, 2407 2408-14,08,1.057448,0.039174, 2409-13,08,1.059054,0.044041, 2410-12,08,1.060352,0.049644, 2411-11,08,1.061159,0.056057, 2412-10,08,1.061235,0.063322, 2413 2414-14,09,1.053021,0.040580, 2415-13,09,1.053997,0.045176, 2416-12,09,1.054606,0.050359, 2417-11,09,1.054687,0.056158, 2418-10,09,1.054046,0.062566, 2419 2420-14,10,1.048834,0.041444, 2421-13,10,1.049303,0.045719, 2422-12,10,1.049380,0.050452, 2423-11,10,1.048933,0.055640, 2424-10,10,1.047807,0.061249, 2425 2426-14,11,1.044928,0.041867, 2427-13,11,1.044997,0.045801, 2428-12,11,1.044674,0.050084, 2429-11,11,1.043853,0.054695, 2430-10,11,1.042417,0.059584, 2431 2432-14,12,1.041320,0.041938, 2433-13,12,1.041080,0.045531, 2434-12,12,1.040464,0.049384, 2435-11,12,1.039389,0.053465, 2436-10,12,1.037766,0.057719, 2437 2438-14,13,1.038010,0.041734, 2439-13,13,1.037537,0.044999, 2440-12,13,1.036713,0.048452, 2441-11,13,1.035473,0.052056, 2442-10,13,1.033752,0.055758, 2443 2444-14,14,1.034989,0.041321, 2445-13,14,1.034344,0.044277, 2446-12,14,1.033378,0.047365, 2447-11,14,1.032040,0.050547, 2448-10,14,1.030282,0.053773, 2449 2450-14,15,1.032241,0.040751, 2451-13,15,1.031474,0.043422, 2452-12,15,1.030414,0.046180, 2453-11,15,1.029026,0.048991, 2454-10,15,1.027274,0.051808, 2455 2456-14,16,1.029747,0.040066, 2457-13,16,1.028895,0.042477, 2458-12,16,1.027781,0.044941, 2459-11,16,1.026377,0.047428, 2460-10,16,1.024658,0.049894, 2461 2462-14,17,1.027486,0.039301, 2463-13,17,1.026579,0.041475, 2464-12,17,1.025438,0.043679, 2465-11,17,1.024043,0.045883, 2466-10,17,1.022375,0.048049, 2467 2468-14,18,1.025437,0.038481, 2469-13,18,1.024499,0.040444, 2470-12,18,1.023352,0.042417, 2471-11,18,1.021981,0.044374, 2472-10,18,1.020375,0.046282, 2473 2474-14,19,1.023580,0.037629, 2475-13,19,1.022628,0.039401, 2476-12,19,1.021489,0.041170, 2477-11,19,1.020155,0.042912, 2478-10,19,1.018617,0.044599, 2479 2480-14,20,1.021896,0.036759, 2481-13,20,1.020942,0.038361, 2482-12,20,1.019824,0.039950, 2483-11,20,1.018533,0.041505, 2484-10,20,1.017066,0.043001, 2485 2486-09,00,1.152759,0.003489, 2487-08,00,1.181848,0.008431, 2488-07,00,1.222408,0.020053, 2489-06,00,1.278884,0.046723, 2490-05,00,1.353831,0.105839, 2491 2492-09,01,1.146232,0.026376, 2493-08,01,1.169677,0.038841, 2494-07,01,1.199049,0.060219, 2495-06,01,1.233798,0.097331, 2496-05,01,1.268723,0.160826, 2497 2498-09,02,1.134679,0.044579, 2499-08,02,1.151385,0.060814, 2500-07,02,1.169639,0.085335, 2501-06,02,1.186778,0.122162, 2502-05,02,1.196351,0.175646, 2503 2504-09,03,1.120694,0.057595, 2505-08,03,1.131255,0.074701, 2506-07,03,1.140733,0.098259, 2507-06,03,1.146266,0.130005, 2508-05,03,1.142853,0.170672, 2509 2510-09,04,1.106249,0.065948, 2511-08,04,1.111968,0.082156, 2512-07,04,1.115404,0.102861, 2513-06,04,1.114273,0.128440, 2514-05,04,1.105376,0.158134, 2515 2516-09,05,1.092564,0.070592, 2517-08,05,1.094818,0.085055, 2518-07,05,1.094475,0.102411, 2519-06,05,1.089952,0.122397, 2520-05,05,1.079407,0.143879, 2521 2522-09,06,1.080246,0.072520, 2523-08,06,1.080188,0.084987, 2524-07,06,1.077672,0.099188, 2525-06,06,1.071684,0.114638, 2526-05,06,1.061236,0.130280, 2527 2528-09,07,1.069494,0.072580, 2529-08,07,1.067987,0.083120, 2530-07,07,1.064339,0.094618, 2531-06,07,1.057935,0.106568, 2532-05,07,1.048279,0.118116, 2533 2534-09,08,1.060276,0.071425, 2535-08,08,1.057920,0.080250, 2536-07,08,1.053778,0.089537, 2537-06,08,1.047493,0.098840, 2538-05,08,1.038838,0.107508, 2539 2540-09,09,1.052450,0.069523, 2541-08,09,1.049645,0.076885, 2542-07,09,1.045382,0.084405, 2543-06,09,1.039464,0.091717, 2544-05,09,1.031806,0.098337, 2545 2546-09,10,1.045832,0.067197, 2547-08,10,1.042834,0.073340, 2548-07,10,1.038659,0.079462, 2549-06,10,1.033205,0.085271, 2550-05,10,1.026459,0.090413, 2551 2552-09,11,1.040241,0.064664, 2553-08,11,1.037210,0.069803, 2554-07,11,1.033231,0.074821, 2555-06,11,1.028260,0.079488, 2556-05,11,1.022317,0.083544, 2557 2558-09,12,1.035508,0.062063, 2559-08,12,1.032539,0.066381, 2560-07,12,1.028808,0.070524, 2561-06,12,1.024300,0.074315, 2562-05,12,1.019052,0.077561, 2563 2564-09,13,1.031490,0.059482, 2565-08,13,1.028638,0.063128, 2566-07,13,1.025171,0.066576, 2567-06,13,1.021090,0.069688, 2568-05,13,1.016439,0.072320, 2569 2570-09,14,1.028065,0.056975, 2571-08,14,1.025359,0.060070, 2572-07,14,1.022152,0.062962, 2573-06,14,1.018458,0.065542, 2574-05,14,1.014319,0.067702, 2575 2576-09,15,1.025132,0.054573, 2577-08,15,1.022583,0.057215, 2578-07,15,1.019626,0.059658, 2579-06,15,1.016277,0.061817, 2580-05,15,1.012577,0.063610, 2581 2582-09,16,1.022608,0.052291, 2583-08,16,1.020219,0.054559, 2584-07,16,1.017494,0.056638, 2585-06,16,1.014452,0.058460, 2586-05,16,1.011130,0.059962, 2587 2588-09,17,1.020426,0.050135, 2589-08,17,1.018192,0.052094, 2590-07,17,1.015681,0.053874, 2591-06,17,1.012912,0.055424, 2592-05,17,1.009915,0.056694, 2593 2594-09,18,1.018530,0.048106, 2595-08,18,1.016444,0.049806, 2596-07,18,1.014129,0.051341, 2597-06,18,1.011600,0.052670, 2598-05,18,1.008887,0.053752, 2599 2600-09,19,1.016874,0.046201, 2601-08,19,1.014929,0.047684, 2602-07,19,1.012790,0.049015, 2603-06,19,1.010476,0.050161, 2604-05,19,1.008009,0.051092, 2605 2606-09,20,1.015422,0.044413, 2607-08,20,1.013607,0.045714, 2608-07,20,1.011629,0.046875, 2609-06,20,1.009505,0.047870, 2610-05,20,1.007254,0.048675, 2611 2612/* Table 5.6 p. 250 */ 2613 2614-4,00,1.438208,0.230161, 2615-3,00,1.483729,0.469232, 2616-2,00,1.340965,0.850337, 2617-1,00,0.697175,1.155727, 2618/* -0,00,0.577216,0.000000, den Test auf Null verbessern */ 2619 2620-4,01,1.287244,0.263705, 2621-3,01,1.251069,0.410413, 2622-2,01,1.098808,0.561916, 2623-1,01,0.813486,0.578697, 2624-0,01,0.621450,0.343378, 2625 2626-4,02,1.185758,0.247356, 2627-3,02,1.136171,0.328439, 2628-2,02,1.032990,0.388428, 2629-1,02,0.896419,0.378838, 2630-0,02,0.798042,0.289091, 2631 2632-4,03,1.123282,0.217835, 2633-3,03,1.080316,0.262814, 2634-2,03,1.013205,0.289366, 2635-1,03,0.936283,0.280906, 2636-0,03,0.875873,0.237665, 2637 2638-4,04,1.085153,0.189003, 2639-3,04,1.051401,0.215118, 2640-2,04,1.006122,0.228399, 2641-1,04,0.957446,0.222612, 2642-0,04,0.916770,0.198713, 2643 2644-4,05,1.061263,0.164466, 2645-3,05,1.035185,0.180487, 2646-2,05,1.003172,0.187857, 2647-1,05,0.969809,0.183963, 2648-0,05,0.940714,0.169481, 2649 2650-4,06,1.045719,0.144391, 2651-3,06,1.025396,0.154746, 2652-2,06,1.001788,0.159189, 2653-1,06,0.977582,0.156511, 2654-0,06,0.955833,0.147129, 2655 2656-4,07,1.035205,0.128073, 2657-3,07,1.019109,0.135079, 2658-2,07,1.001077,0.137939, 2659-1,07,0.982756,0.136042, 2660-0,07,0.965937,0.129646, 2661 2662-4,08,1.027834,0.114732, 2663-3,08,1.014861,0.119660, 2664-2,08,1.000684,0.121599, 2665-1,08,0.986356,0.120218, 2666-0,08,0.972994,0.115678, 2667 2668-4,09,1.022501,0.103711, 2669-3,09,1.011869,0.107294, 2670-2,09,1.000454,0.108665, 2671-1,09,0.988955,0.107634, 2672-0,09,0.978103,0.104303, 2673 2674-4,10,1.018534,0.094502, 2675-3,10,1.009688,0.097181, 2676-2,10,1.000312,0.098184, 2677-1,10,0.990887,0.097396, 2678-0,10,0.981910,0.094885, 2679 2680-4,11,1.015513,0.086718, 2681-3,11,1.008052,0.088770, 2682-2,11,1.000221,0.089525, 2683-1,11,0.992361,0.088911, 2684-0,11,0.984819,0.086975, 2685 2686-4,12,1.013163,0.080069, 2687-3,12,1.006795,0.081673, 2688-2,12,1.000161,0.082255, 2689-1,12,0.993508,0.081769, 2690-0,12,0.987088,0.080245, 2691 2692-4,13,1.011303,0.074333, 2693-3,13,1.005809,0.075609, 2694-2,13,1.000119,0.076067, 2695-1,13,0.994418,0.075676, 2696-0,13,0.988891,0.074457, 2697 2698-4,14,1.009806,0.069340, 2699-3,14,1.005022,0.070371, 2700-2,14,1.000090,0.070738, 2701-1,14,0.995151,0.070419, 2702-0,14,0.990345,0.069429, 2703 2704-4,15,1.008585,0.064959, 2705-3,15,1.004384,0.065803, 2706-2,15,1.000070,0.066102, 2707-1,15,0.995751,0.065838, 2708-0,15,0.991534,0.065024, 2709 2710-4,16,1.007577,0.061086, 2711-3,16,1.003859,0.061786, 2712-2,16,1.000055,0.062032, 2713-1,16,0.996246,0.061812, 2714-0,16,0.992518,0.061135, 2715 2716-4,17,1.006735,0.057640, 2717-3,17,1.003423,0.058227, 2718-2,17,1.000043,0.058432, 2719-1,17,0.996661,0.058246, 2720-0,17,0.993342,0.057677, 2721 2722-4,18,1.006025,0.054555, 2723-3,18,1.003057,0.055052, 2724-2,18,1.000035,0.055224, 2725-1,18,0.997011,0.055066, 2726-0,18,0.994038,0.054583, 2727 2728-4,19,1.005420,0.051779, 2729-3,19,1.002747,0.052202, 2730-2,19,1.000028,0.052349, 2731-1,19,0.997309,0.052214, 2732-0,19,0.994631,0.051801, 2733 2734-4,20,1.004902,0.049267, 2735-3,20,1.002481,0.049631, 2736-2,20,1.000023,0.049757, 2737-1,20,0.997565,0.049640, 2738-0,20,0.995140,0.049284, 2739 274001,00,0.596347,0.000000, 274102,00,0.722657,0.000000, 274203,00,0.786251,0.000000, 274304,00,0.825383,0.000000, 274405,00,0.852111,0.000000, 2745 274601,01,0.673321,0.147864, 274702,01,0.747012,0.075661, 274803,01,0.797036,0.045686, 274904,01,0.831126,0.030619, 275005,01,0.855544,0.021985, 2751 275201,02,0.777514,0.186570, 275302,02,0.796965,0.118228, 275403,02,0.823055,0.078753, 275504,02,0.846097,0.055494, 275605,02,0.864880,0.040999, 2757 275801,03,0.847468,0.181226, 275902,03,0.844361,0.132252, 276003,03,0.853176,0.096659, 276104,03,0.865521,0.072180, 276205,03,0.877860,0.055341, 2763 276401,04,0.891460,0.165207, 276502,04,0.881036,0.131686, 276603,04,0.880584,0.103403, 276704,04,0.885308,0.081408, 276805,04,0.892143,0.064825, 2769 277001,05,0.919826,0.148271, 277102,05,0.907873,0.125136, 277203,05,0.903152,0.103577, 277304,05,0.903231,0.085187, 277405,05,0.906058,0.070209, 2775 277601,06,0.938827,0.132986, 277702,06,0.927384,0.116656, 277803,06,0.921006,0.100357, 277904,06,0.918527,0.085460, 278005,06,0.918708,0.072544, 2781 278201,07,0.952032,0.119807, 278302,07,0.941722,0.107990, 278403,07,0.934958,0.095598, 278504,07,0.931209,0.083666, 278605,07,0.929765,0.072792, 2787 278801,08,0.961512,0.108589, 278902,08,0.952435,0.099830, 279003,08,0.945868,0.090303, 279104,08,0.941594,0.080755, 279205,08,0.939221,0.071700, 2793 279401,09,0.968512,0.099045, 279502,09,0.960582,0.092408, 279603,09,0.954457,0.084986, 279704,09,0.950072,0.077313, 279805,09,0.947219,0.069799, 2799 280001,10,0.973810,0.090888, 280102,10,0.966885,0.085758, 280203,10,0.961283,0.079898, 280304,10,0.957007,0.073688, 280405,10,0.953955,0.067447, 2805 280601,11,0.977904,0.083871, 280702,11,0.971842,0.079836, 280803,11,0.966766,0.075147, 280904,11,0.962708,0.070080, 281005,11,0.959626,0.064878, 2811 281201,12,0.981127,0.077790, 281302,12,0.975799,0.074567, 281403,12,0.971216,0.070769, 281504,12,0.967423,0.066599, 281605,12,0.964412,0.062242, 2817 281801,13,0.983706,0.072484, 281902,13,0.979000,0.069873, 282003,13,0.974865,0.066762, 282104,13,0.971351,0.063300, 282205,13,0.968464,0.059630, 2823 282401,14,0.985799,0.067822, 282502,14,0.981621,0.065679, 282603,14,0.977888,0.063104, 282704,14,0.974646,0.060206, 282805,14,0.971911,0.057096, 2829 283001,15,0.987519,0.063698, 283102,15,0.983791,0.061921, 283203,15,0.980414,0.059767, 283304,15,0.977430,0.057322, 283405,15,0.974858,0.054671, 2835 283601,16,0.988949,0.060029, 283702,16,0.985606,0.058539, 283803,16,0.982544,0.056723, 283904,16,0.979799,0.054644, 284005,16,0.977391,0.052371, 2841 284201,17,0.990149,0.056745, 284302,17,0.987138,0.055485, 284403,17,0.984353,0.053941, 284504,17,0.981827,0.052162, 284605,17,0.979579,0.050200, 2847 284801,18,0.991167,0.053792, 284902,18,0.988442,0.052717, 285003,18,0.985902,0.051394, 285104,18,0.983574,0.049861, 285205,18,0.981478,0.048160, 2853 285401,19,0.992036,0.051122, 285502,19,0.989561,0.050199, 285603,19,0.987237,0.049057, 285704,19,0.985089,0.047728, 285805,19,0.983135,0.046245, 2859 286001,20,0.992784,0.048699, 286102,20,0.990527,0.047900, 286203,20,0.988395,0.046909, 286304,20,0.986410,0.045749, 286405,20,0.984587,0.044449, 2865 286606,00,0.871606,0.000000, 286707,00,0.886488,0.000000, 286808,00,0.898237,0.000000, 286909,00,0.907758,0.000000, 287010,00,0.915633,0.000000, 2871 287206,01,0.873827,0.016570, 287307,01,0.888009,0.012947, 287408,01,0.899327,0.010401, 287509,01,0.908565,0.008543, 287610,01,0.916249,0.007143, 2877 287806,02,0.880023,0.031454, 287907,02,0.892327,0.024866, 288008,02,0.902453,0.020140, 288109,02,0.910901,0.016639, 288210,02,0.918040,0.013975, 2883 288406,03,0.889029,0.043517, 288507,03,0.898793,0.034995, 288608,03,0.907236,0.028693, 288709,03,0.914531,0.023921, 288810,03,0.920856,0.020230, 2889 289006,04,0.899484,0.052380, 289107,04,0.906591,0.042967, 289208,04,0.913167,0.035755, 289309,04,0.919127,0.030145, 289410,04,0.924479,0.025717, 2895 289606,05,0.910242,0.058259, 289707,05,0.914952,0.048780, 289808,05,0.919729,0.041242, 289909,05,0.924336,0.035208, 290010,05,0.928664,0.030334, 2901 290206,06,0.920534,0.061676, 290307,06,0.923283,0.052667, 290408,06,0.926481,0.045242, 290509,06,0.929836,0.039123, 290610,06,0.933175,0.034063, 2907 290806,07,0.929945,0.063220, 290907,07,0.931193,0.054971, 291008,07,0.933096,0.047942, 291109,07,0.935365,0.041986, 291210,07,0.937807,0.036944, 2913 291406,08,0.938313,0.063425, 291507,08,0.938469,0.056047, 291608,08,0.939359,0.049570, 291709,08,0.940731,0.043936, 291810,08,0.942398,0.039060, 2919 292006,09,0.945629,0.062714, 292107,09,0.945023,0.056211, 292208,09,0.945154,0.050349, 292309,09,0.945812,0.045128, 292410,09,0.946833,0.040514, 2925 292606,10,0.951965,0.061408, 292707,10,0.950850,0.055725, 292808,10,0.950427,0.050481, 292909,10,0.950535,0.045711, 293010,10,0.951035,0.041413, 2931 293206,11,0.957427,0.059735, 293307,11,0.955987,0.054790, 293408,11,0.955176,0.050135, 293509,11,0.954870,0.045818, 293610,11,0.954959,0.041861, 2937 293806,12,0.962128,0.057855, 293907,12,0.960495,0.053560, 294008,12,0.959421,0.049444, 294109,12,0.958814,0.045563, 294210,12,0.958586,0.041948, 2943 294406,13,0.966178,0.055877, 294507,13,0.964444,0.052146, 294608,13,0.963201,0.048514, 294709,13,0.962379,0.045038, 294810,13,0.961913,0.041755, 2949 295006,14,0.969673,0.053874, 295107,14,0.967903,0.050627, 295208,14,0.966559,0.047425, 295309,14,0.965591,0.044319, 295410,14,0.964949,0.041347, 2955 295606,15,0.972699,0.051894, 295707,15,0.970935,0.049062, 295808,15,0.969539,0.046236, 295909,15,0.968477,0.043463, 296010,15,0.967710,0.040780, 2961 296206,16,0.975326,0.049966, 296307,16,0.973597,0.047489, 296408,16,0.972185,0.044992, 296509,16,0.971067,0.042516, 296610,16,0.970214,0.040095, 2967 296806,17,0.977617,0.048109, 296907,17,0.975940,0.045935, 297008,17,0.974538,0.043724, 297109,17,0.973393,0.041512, 297210,17,0.972484,0.039329, 2973 297406,18,0.979622,0.046332, 297507,18,0.978009,0.044419, 297608,18,0.976632,0.042456, 297709,18,0.975481,0.040477, 297810,18,0.974540,0.038508, 2979 298006,19,0.981384,0.044641, 298107,19,0.979839,0.042951, 298208,19,0.978500,0.041205, 298309,19,0.977357,0.039431, 298410,19,0.976402,0.037653, 2985 298606,20,0.982938,0.043036, 298707,20,0.981465,0.041538, 298808,20,0.980169,0.039980, 298909,20,0.979047,0.038388, 299010,20,0.978090,0.036781, 2991 2992/* Table 5.6 p. 251 */ 2993 299411,00,0.922260,0.000000, 299512,00,0.927914,0.000000, 299613,00,0.932796,0.000000, 299714,00,0.937055,0.000000, 299815,00,0.940804,0.000000, 2999 300011,01,0.922740,0.006063, 300112,01,0.928295,0.005212, 300213,01,0.933105,0.004528, 300314,01,0.937308,0.003972, 300415,01,0.941014,0.003512, 3005 300611,02,0.924143,0.011902, 300712,02,0.929416,0.010258, 300813,02,0.934013,0.008932, 300914,02,0.938055,0.007847, 301015,02,0.941636,0.006949, 3011 301211,03,0.926370,0.017321, 301312,03,0.931205,0.014991, 301413,03,0.935473,0.013098, 301514,03,0.939261,0.011540, 301615,03,0.942643,0.010242, 3017 301811,04,0.929270,0.022171, 301912,04,0.933560,0.019295, 302013,04,0.937408,0.016934, 302114,04,0.940870,0.014974, 302215,04,0.943994,0.013331, 3023 302411,05,0.932672,0.026361, 302512,05,0.936356,0.023091, 302613,05,0.939729,0.020373, 302714,05,0.942816,0.018095, 302815,05,0.945640,0.016169, 3029 303011,06,0.936400,0.029857, 303112,06,0.939462,0.026339, 303213,06,0.942338,0.023378, 303314,06,0.945024,0.020867, 303415,06,0.947522,0.018725, 3035 303611,07,0.940297,0.032670, 303712,07,0.942757,0.029036, 303813,07,0.945140,0.025934, 303914,07,0.947419,0.023273, 304015,07,0.949582,0.020980, 3041 304211,08,0.944229,0.034847, 304312,08,0.946132,0.031205, 304413,08,0.948047,0.028052, 304514,08,0.949933,0.025315, 304615,08,0.951765,0.022931, 3047 304811,09,0.948093,0.036453, 304912,09,0.949500,0.032887, 305013,09,0.950985,0.029756, 305114,09,0.952502,0.027004, 305215,09,0.954018,0.024582, 3053 305411,10,0.951816,0.037566, 305512,10,0.952792,0.034134, 305613,10,0.953895,0.031081, 305714,10,0.955075,0.028365, 305815,10,0.956296,0.025949, 3059 306011,11,0.955347,0.038261, 306112,11,0.955958,0.035004, 306213,11,0.956729,0.032068, 306314,11,0.957610,0.029426, 306415,11,0.958563,0.027052, 3065 306611,12,0.958659,0.038612, 306712,12,0.958968,0.035552, 306813,12,0.959454,0.032761, 306914,12,0.960073,0.030221, 307015,12,0.960787,0.027915, 3071 307211,13,0.961739,0.038684, 307312,13,0.961800,0.035833, 307413,13,0.962049,0.033201, 307514,13,0.962443,0.030781, 307615,13,0.962947,0.028564, 3077 307811,14,0.964583,0.038534, 307912,14,0.964447,0.035893, 308013,14,0.964499,0.033428, 308114,14,0.964702,0.031140, 308215,14,0.965026,0.029024, 3083 308411,15,0.967199,0.038211, 308512,15,0.966907,0.035775, 308613,15,0.966799,0.033479, 308714,15,0.966843,0.031327, 308815,15,0.967011,0.029320, 3089 309011,16,0.969597,0.037756, 309112,16,0.969184,0.035515, 309213,16,0.968947,0.033384, 309314,16,0.968860,0.031370, 309415,16,0.968897,0.029476, 3095 309611,17,0.971789,0.037200, 309712,17,0.971285,0.035144, 309813,17,0.970946,0.033172, 309914,17,0.970752,0.031293, 310015,17,0.970680,0.029512, 3101 310211,18,0.973792,0.036572, 310312,18,0.973220,0.034687, 310413,18,0.972802,0.032865, 310514,18,0.972521,0.031117, 310615,18,0.972359,0.029448, 3107 310811,19,0.975621,0.035893, 310912,19,0.974999,0.034166, 311013,19,0.974521,0.032485, 311114,19,0.974172,0.030862, 311215,19,0.973936,0.029301, 3113 311411,20,0.977290,0.035179, 311512,20,0.976634,0.033597, 311613,20,0.976112,0.032049, 311714,20,0.975709,0.030542, 311815,20,0.975414,0.029086, 3119 312016,00,0.944130,0.000000, 312117,00,0.947100,0.000000, 312218,00,0.949769,0.000000, 312319,00,0.952181,0.000000, 312420,00,0.954371,0.000000, 3125 312616,01,0.944306,0.003128, 312717,01,0.947250,0.002804, 312818,01,0.949897,0.002527, 312919,01,0.952291,0.002290, 313020,01,0.954467,0.002085, 3131 313216,02,0.944829,0.006196, 313317,02,0.947693,0.005560, 313418,02,0.950277,0.005016, 313519,02,0.952619,0.004549, 313620,02,0.954752,0.004144, 3137 313816,03,0.945678,0.009150, 313917,03,0.948416,0.008223, 314018,03,0.950898,0.007430, 314119,03,0.953156,0.006745, 314220,03,0.955219,0.006151, 3143 314416,04,0.946824,0.011940, 314517,04,0.949395,0.010754, 314618,04,0.951741,0.009735, 314719,04,0.953887,0.008853, 314820,04,0.955856,0.008084, 3149 315016,05,0.948226,0.014529, 315117,05,0.950600,0.013121, 315218,05,0.952782,0.011904, 315319,05,0.954793,0.010847, 315420,05,0.956650,0.009922, 3155 315616,06,0.949842,0.016886, 315717,06,0.951995,0.015296, 315818,06,0.953995,0.013916, 315919,06,0.955853,0.012709, 316020,06,0.957581,0.011649, 3161 316216,07,0.951624,0.018994, 316317,07,0.953545,0.017265, 316418,07,0.955349,0.015753, 316519,07,0.957043,0.014425, 316620,07,0.958631,0.013253, 3167 316816,08,0.953527,0.020847, 316917,08,0.955212,0.019019, 317018,08,0.956815,0.017409, 317119,08,0.958337,0.015986, 317220,08,0.959779,0.014723, 3173 317416,09,0.955509,0.022445, 317517,09,0.956960,0.020555, 317618,09,0.958363,0.018878, 317719,09,0.959712,0.017387, 317820,09,0.961004,0.016056, 3179 318016,10,0.957530,0.023797, 318117,10,0.958758,0.021878, 318218,10,0.959966,0.020163, 318319,10,0.961144,0.018628, 318420,10,0.962288,0.017250, 3185 318616,11,0.959559,0.024917, 318717,11,0.960576,0.022998, 318818,11,0.961598,0.021270, 318919,11,0.962612,0.019712, 319020,11,0.963611,0.018305, 3191 319216,12,0.961568,0.025823, 319317,12,0.962391,0.023927, 319418,12,0.963238,0.022207, 319519,12,0.964097,0.020645, 319620,12,0.964956,0.019227, 3197 319816,13,0.963534,0.026534, 319917,13,0.964181,0.024679, 320018,13,0.964868,0.022984, 320119,13,0.965582,0.021436, 320220,13,0.966310,0.020021, 3203 320416,14,0.965443,0.027070, 320517,14,0.965931,0.025271, 320618,14,0.966472,0.023616, 320719,14,0.967052,0.022094, 320820,14,0.967658,0.020694, 3209 321016,15,0.967280,0.027453, 321117,15,0.967628,0.025720, 321218,15,0.968039,0.024114, 321319,15,0.968496,0.022629, 321420,15,0.968990,0.021255, 3215 321616,16,0.969038,0.027700, 321717,16,0.969264,0.026041, 321818,16,0.969558,0.024493, 321919,16,0.969906,0.023052, 322020,16,0.970297,0.021712, 3221 322216,17,0.970712,0.027831, 322317,17,0.970832,0.026249, 322418,17,0.971023,0.024765, 322519,17,0.971273,0.023375, 322620,17,0.971571,0.022075, 3227 322816,18,0.972300,0.027862, 322917,18,0.972328,0.026361, 323018,18,0.972430,0.024943, 323119,18,0.972594,0.023607, 323220,18,0.972808,0.022352, 3233 323416,19,0.973800,0.027809, 323517,19,0.973751,0.026388, 323618,19,0.973775,0.025038, 323719,19,0.973863,0.023760, 323820,19,0.974004,0.022552, 3239 324016,20,0.975215,0.027685, 324117,20,0.975099,0.026343, 324218,20,0.975057,0.025062, 324319,20,0.975079,0.023842, 324420,20,0.975155,0.022684 3245]),done); 3246done; 3247 3248test_complex_table(lambda([z],z*%e^z*expintegral_e1(z)),'ec_1,838,1.25e-6); 3249[]; 3250 3251kill(all); 3252done; 3253 3254/*****************************************************************************/ 3255