1## Copyright (C) 2016, 2017 Julien Bect <jbect@users.sourceforge.net> 2## Copyright (C) 2016 Susi Lehtola 3## Copyright (C) 2004 Teemu Ikonen <tpikonen@pcu.helsinki.fi> 4## 5## This program is free software; you can redistribute it and/or modify 6## it under the terms of the GNU General Public License as published by 7## the Free Software Foundation; either version 2 of the License, or 8## (at your option) any later version. 9## 10## This program is distributed in the hope that it will be useful, 11## but WITHOUT ANY WARRANTY; without even the implied warranty of 12## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13## GNU General Public License for more details. 14## 15## You should have received a copy of the GNU General Public License 16## along with this program; if not, see <http://www.gnu.org/licenses/>. 17 18RT="./replace_template.sh" 19 20cp gsl_sf.header.cc gsl_sf.cc 21 22# double to double ################################################### 23 24export octave_name=gsl_sf_clausen 25export funcname=gsl_sf_clausen_e 26cat << \EOF > docstring.txt 27The Clausen function is defined by the following integral, 28 29Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2)) 30 31It is related to the dilogarithm by Cl_2(\theta) = \Im Li_2(\exp(i \theta)). 32EOF 33${RT} D_D >> gsl_sf.cc 34 35## Deprecated naming scheme 36export octave_name=clausen 37export funcname=gsl_sf_clausen_e 38${RT} D_D >> gsl_sf.cc 39 40###################################################################### 41 42export octave_name=gsl_sf_dawson 43export funcname=gsl_sf_dawson_e 44cat << \EOF > docstring.txt 45The Dawson integral is defined by \exp(-x^2) \int_0^x dt \exp(t^2). 46A table of Dawson integral can be found in Abramowitz & Stegun, Table 7.5. 47EOF 48${RT} D_D >> gsl_sf.cc 49 50## Deprecated naming scheme 51export octave_name=dawson 52export funcname=gsl_sf_dawson_e 53${RT} D_D >> gsl_sf.cc 54 55###################################################################### 56 57export octave_name=gsl_sf_debye_1 58export funcname=gsl_sf_debye_1_e 59cat << \EOF > docstring.txt 60The Debye functions are defined by the integral 61 62D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). 63 64For further information see Abramowitz & Stegun, Section 27.1. 65EOF 66${RT} D_D >> gsl_sf.cc 67 68## Deprecated naming scheme 69export octave_name=debye_1 70export funcname=gsl_sf_debye_1_e 71${RT} D_D >> gsl_sf.cc 72 73###################################################################### 74 75export octave_name=gsl_sf_debye_2 76export funcname=gsl_sf_debye_2_e 77cat << \EOF > docstring.txt 78The Debye functions are defined by the integral 79 80D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). 81 82For further information see Abramowitz & Stegun, Section 27.1. 83EOF 84${RT} D_D >> gsl_sf.cc 85 86## Deprecated naming scheme 87export octave_name=debye_2 88export funcname=gsl_sf_debye_2_e 89${RT} D_D >> gsl_sf.cc 90 91###################################################################### 92 93export octave_name=gsl_sf_debye_3 94export funcname=gsl_sf_debye_3_e 95cat << \EOF > docstring.txt 96The Debye functions are defined by the integral 97 98D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). 99 100For further information see Abramowitz & Stegun, Section 27.1. 101EOF 102${RT} D_D >> gsl_sf.cc 103 104## Deprecated naming scheme 105export octave_name=debye_3 106export funcname=gsl_sf_debye_3_e 107${RT} D_D >> gsl_sf.cc 108 109###################################################################### 110 111export octave_name=gsl_sf_debye_4 112export funcname=gsl_sf_debye_4_e 113cat << \EOF > docstring.txt 114The Debye functions are defined by the integral 115 116D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). 117 118For further information see Abramowitz & Stegun, Section 27.1. 119EOF 120${RT} D_D >> gsl_sf.cc 121 122## Deprecated naming scheme 123export octave_name=debye_4 124export funcname=gsl_sf_debye_4_e 125${RT} D_D >> gsl_sf.cc 126 127###################################################################### 128 129export octave_name=gsl_sf_debye_5 130export funcname=gsl_sf_debye_5_e 131cat << \EOF > docstring.txt 132The Debye functions are defined by the integral 133 134D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). 135 136For further information see Abramowitz & Stegun, Section 27.1. 137EOF 138${RT} D_D >> gsl_sf.cc 139 140###################################################################### 141 142export octave_name=gsl_sf_debye_6 143export funcname=gsl_sf_debye_6_e 144cat << \EOF > docstring.txt 145The Debye functions are defined by the integral 146 147D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)). 148 149For further information see Abramowitz & Stegun, Section 27.1. 150EOF 151${RT} D_D >> gsl_sf.cc 152 153###################################################################### 154 155export octave_name=gsl_sf_dilog 156export funcname=gsl_sf_dilog_e 157cat << \EOF > docstring.txt 158Computes the dilogarithm for a real argument. 159In Lewin’s notation this is Li_2(x), the real part of the 160dilogarithm of a real x. It is defined by the integral 161representation 162 163 Li_2(x) = - \Re \int_0^x ds \log(1-s) / s. 164 165Note that \Im(Li_2(x)) = 0 for x <= 1, and -\pi\log(x) 166for x > 1. 167 168Note that Abramowitz & Stegun refer to the Spence integral 169S(x)=Li_2(1-x) as the dilogarithm rather than Li_2(x). 170EOF 171${RT} D_D >> gsl_sf.cc 172 173###################################################################### 174 175export octave_name=gsl_sf_erf 176export funcname=gsl_sf_erf_e 177cat << \EOF > docstring.txt 178Computes the error function 179erf(x) = (2/\sqrt(\pi)) \int_0^x dt \exp(-t^2). 180EOF 181${RT} D_D >> gsl_sf.cc 182 183## Deprecated naming scheme 184export octave_name=erf_gsl 185export funcname=gsl_sf_erf_e 186${RT} D_D >> gsl_sf.cc 187 188###################################################################### 189 190export octave_name=gsl_sf_erfc 191export funcname=gsl_sf_erfc_e 192cat << \EOF > docstring.txt 193Computes the complementary error function 194erfc(x) = 1 - erf(x) = (2/\sqrt(\pi)) \int_x^\infty \exp(-t^2). 195EOF 196${RT} D_D >> gsl_sf.cc 197 198## Deprecated naming scheme 199export octave_name=erfc_gsl 200export funcname=gsl_sf_erfc_e 201${RT} D_D >> gsl_sf.cc 202 203###################################################################### 204 205export octave_name=gsl_sf_log_erfc 206export funcname=gsl_sf_log_erfc_e 207cat << \EOF > docstring.txt 208Computes the logarithm of the complementary error 209function \log(\erfc(x)). 210EOF 211${RT} D_D >> gsl_sf.cc 212 213## Deprecated naming scheme 214export octave_name=log_erfc 215export funcname=gsl_sf_log_erfc_e 216${RT} D_D >> gsl_sf.cc 217 218###################################################################### 219 220export octave_name=gsl_sf_erf_Z 221export funcname=gsl_sf_erf_Z_e 222cat << \EOF > docstring.txt 223Computes the Gaussian probability function 224Z(x) = (1/(2\pi)) \exp(-x^2/2). 225EOF 226${RT} D_D >> gsl_sf.cc 227 228## Deprecated naming scheme 229export octave_name=erf_Z 230export funcname=gsl_sf_erf_Z_e 231${RT} D_D >> gsl_sf.cc 232 233###################################################################### 234 235export octave_name=gsl_sf_erf_Q 236export funcname=gsl_sf_erf_Q_e 237cat << \EOF > docstring.txt 238Computes the upper tail of the Gaussian probability 239function Q(x) = (1/(2\pi)) \int_x^\infty dt \exp(-t^2/2). 240EOF 241${RT} D_D >> gsl_sf.cc 242 243## Deprecated naming scheme 244export octave_name=erf_Q 245export funcname=gsl_sf_erf_Q_e 246${RT} D_D >> gsl_sf.cc 247 248###################################################################### 249 250export octave_name=gsl_sf_hazard 251export funcname=gsl_sf_hazard_e 252cat << \EOF > docstring.txt 253The hazard function for the normal distrbution, also known as the 254inverse Mill\'s ratio, is defined as 255h(x) = Z(x)/Q(x) = \sqrt@{2/\pi \exp(-x^2 / 2) / \erfc(x/\sqrt 2)@}. 256It decreases rapidly as x approaches -\infty and asymptotes to 257h(x) \sim x as x approaches +\infty. 258EOF 259${RT} D_D >> gsl_sf.cc 260 261## Deprecated naming scheme 262export octave_name=hazard 263export funcname=gsl_sf_hazard_e 264${RT} D_D >> gsl_sf.cc 265 266###################################################################### 267 268export octave_name=gsl_sf_expm1 269export funcname=gsl_sf_expm1_e 270cat << \EOF > docstring.txt 271Computes the quantity \exp(x)-1 using an algorithm that 272is accurate for small x. 273EOF 274${RT} D_D >> gsl_sf.cc 275 276## Deprecated naming scheme 277export octave_name=expm1 278export funcname=gsl_sf_expm1_e 279${RT} D_D >> gsl_sf.cc 280 281###################################################################### 282 283export octave_name=gsl_sf_exprel 284export funcname=gsl_sf_exprel_e 285cat << \EOF > docstring.txt 286Computes the quantity (\exp(x)-1)/x using an algorithm 287that is accurate for small x. For small x the algorithm is based on 288the expansion (\exp(x)-1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + \dots. 289EOF 290${RT} D_D >> gsl_sf.cc 291 292## Deprecated naming scheme 293export octave_name=exprel 294export funcname=gsl_sf_exprel_e 295${RT} D_D >> gsl_sf.cc 296 297###################################################################### 298 299export octave_name=gsl_sf_exprel_2 300export funcname=gsl_sf_exprel_2_e 301cat << \EOF > docstring.txt 302Computes the quantity 2(\exp(x)-1-x)/x^2 using an 303algorithm that is accurate for small x. For small x the algorithm is 304based on the expansion 3052(\exp(x)-1-x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + \dots. 306EOF 307${RT} D_D >> gsl_sf.cc 308 309## Deprecated naming scheme 310export octave_name=exprel_2 311export funcname=gsl_sf_exprel_2_e 312${RT} D_D >> gsl_sf.cc 313 314###################################################################### 315 316export octave_name=gsl_sf_expint_E1 317export funcname=gsl_sf_expint_E1_e 318cat << \EOF > docstring.txt 319Computes the exponential integral E_1(x), 320 321E_1(x) := Re \int_1^\infty dt \exp(-xt)/t. 322EOF 323${RT} D_D >> gsl_sf.cc 324 325## Deprecated naming scheme 326export octave_name=expint_E1 327export funcname=gsl_sf_expint_E1_e 328${RT} D_D >> gsl_sf.cc 329 330###################################################################### 331 332export octave_name=gsl_sf_expint_E2 333export funcname=gsl_sf_expint_E2_e 334cat << \EOF > docstring.txt 335Computes the second-order exponential integral E_2(x), 336 337E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2. 338EOF 339${RT} D_D >> gsl_sf.cc 340 341## Deprecated naming scheme 342export octave_name=expint_E2 343export funcname=gsl_sf_expint_E2_e 344${RT} D_D >> gsl_sf.cc 345 346###################################################################### 347 348export octave_name=gsl_sf_expint_Ei 349export funcname=gsl_sf_expint_Ei_e 350cat << \EOF > docstring.txt 351Computes the exponential integral E_i(x), 352 353Ei(x) := - PV(\int_@{-x@}^\infty dt \exp(-t)/t) 354 355where PV denotes the principal value of the integral. 356EOF 357${RT} D_D >> gsl_sf.cc 358 359## Deprecated naming scheme 360export octave_name=expint_Ei 361export funcname=gsl_sf_expint_Ei_e 362${RT} D_D >> gsl_sf.cc 363 364###################################################################### 365 366export octave_name=gsl_sf_Shi 367export funcname=gsl_sf_Shi_e 368cat << \EOF > docstring.txt 369Computes the integral Shi(x) = \int_0^x dt \sinh(t)/t. 370EOF 371${RT} D_D >> gsl_sf.cc 372 373## Deprecated naming scheme 374export octave_name=Shi 375export funcname=gsl_sf_Shi_e 376${RT} D_D >> gsl_sf.cc 377 378###################################################################### 379 380export octave_name=gsl_sf_Chi 381export funcname=gsl_sf_Chi_e 382cat << \EOF > docstring.txt 383Computes the integral 384 385Chi(x) := Re[ \gamma_E + \log(x) + \int_0^x dt (\cosh[t]-1)/t] , 386 387where \gamma_E is the Euler constant. 388EOF 389${RT} D_D >> gsl_sf.cc 390 391## Deprecated naming scheme 392export octave_name=Chi 393export funcname=gsl_sf_Chi_e 394${RT} D_D >> gsl_sf.cc 395 396###################################################################### 397 398export octave_name=gsl_sf_expint_3 399export funcname=gsl_sf_expint_3_e 400cat << \EOF > docstring.txt 401Computes the exponential integral 402Ei_3(x) = \int_0^x dt \exp(-t^3) for x >= 0. 403EOF 404${RT} D_D >> gsl_sf.cc 405 406## Deprecated naming scheme 407export octave_name=expint_3 408export funcname=gsl_sf_expint_3_e 409${RT} D_D >> gsl_sf.cc 410 411###################################################################### 412 413export octave_name=gsl_sf_Si 414export funcname=gsl_sf_Si_e 415cat << \EOF > docstring.txt 416Computes the Sine integral Si(x) = \int_0^x dt \sin(t)/t. 417EOF 418${RT} D_D >> gsl_sf.cc 419 420## Deprecated naming scheme 421export octave_name=Si 422export funcname=gsl_sf_Si_e 423${RT} D_D >> gsl_sf.cc 424 425###################################################################### 426 427export octave_name=gsl_sf_Ci 428export funcname=gsl_sf_Ci_e 429cat << \EOF > docstring.txt 430Computes the Cosine integral 431Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0. 432EOF 433${RT} D_D >> gsl_sf.cc 434 435## Deprecated naming scheme 436export octave_name=Ci 437export funcname=gsl_sf_Ci_e 438${RT} D_D >> gsl_sf.cc 439 440###################################################################### 441 442export octave_name=gsl_sf_atanint 443export funcname=gsl_sf_atanint_e 444cat << \EOF > docstring.txt 445Computes the Arctangent integral 446AtanInt(x) = \int_0^x dt \arctan(t)/t. 447EOF 448${RT} D_D >> gsl_sf.cc 449 450## Deprecated naming scheme 451export octave_name=atanint 452export funcname=gsl_sf_atanint_e 453${RT} D_D >> gsl_sf.cc 454 455###################################################################### 456 457export octave_name=gsl_sf_fermi_dirac_mhalf 458export funcname=gsl_sf_fermi_dirac_mhalf_e 459cat << \EOF > docstring.txt 460Computes the complete Fermi-Dirac integral F_@{-1/2@}(x). 461EOF 462${RT} D_D >> gsl_sf.cc 463 464## Deprecated naming scheme 465export octave_name=fermi_dirac_mhalf 466export funcname=gsl_sf_fermi_dirac_mhalf_e 467${RT} D_D >> gsl_sf.cc 468 469###################################################################### 470 471export octave_name=gsl_sf_fermi_dirac_half 472export funcname=gsl_sf_fermi_dirac_half_e 473cat << \EOF > docstring.txt 474Computes the complete Fermi-Dirac integral F_@{1/2@}(x). 475EOF 476${RT} D_D >> gsl_sf.cc 477 478## Deprecated naming scheme 479export octave_name=fermi_dirac_half 480export funcname=gsl_sf_fermi_dirac_half_e 481${RT} D_D >> gsl_sf.cc 482 483###################################################################### 484 485export octave_name=gsm_sf_fermi_dirac_3half 486export funcname=gsl_sf_fermi_dirac_3half_e 487cat << \EOF > docstring.txt 488Computes the complete Fermi-Dirac integral F_@{3/2@}(x). 489EOF 490${RT} D_D >> gsl_sf.cc 491 492## Deprecated naming scheme 493export octave_name=fermi_dirac_3half 494export funcname=gsl_sf_fermi_dirac_3half_e 495${RT} D_D >> gsl_sf.cc 496 497###################################################################### 498 499export octave_name=gsl_sf_gamma 500export funcname=gsl_sf_gamma_e 501cat << \EOF > docstring.txt 502Computes the Gamma function \Gamma(x), subject to x not 503being a negative integer. The function is computed using the real 504Lanczos method. The maximum value of x such that \Gamma(x) is not 505considered an overflow is given by the macro GSL_SF_GAMMA_XMAX and is 171.0. 506EOF 507${RT} D_D >> gsl_sf.cc 508 509## Deprecated naming scheme 510export octave_name=gamma_gsl 511export funcname=gsl_sf_gamma_e 512${RT} D_D >> gsl_sf.cc 513 514###################################################################### 515 516export octave_name=gsl_sf_lngamma 517export funcname=gsl_sf_lngamma_e 518cat << \EOF > docstring.txt 519Computes the logarithm of the Gamma function, 520\log(\Gamma(x)), subject to x not a being negative integer. 521For x<0 the real part of \log(\Gamma(x)) is returned, which is 522equivalent to \log(|\Gamma(x)|). The function is computed using 523the real Lanczos method. 524EOF 525${RT} D_D >> gsl_sf.cc 526 527## Deprecated naming scheme 528export octave_name=lngamma_gsl 529export funcname=gsl_sf_lngamma_e 530${RT} D_D >> gsl_sf.cc 531 532###################################################################### 533 534export octave_name=gsl_sf_gammastar 535export funcname=gsl_sf_gammastar_e 536cat << \EOF > docstring.txt 537Computes the regulated Gamma Function \Gamma^*(x) 538for x > 0. The regulated gamma function is given by, 539 540\Gamma^*(x) = \Gamma(x)/(\sqrt@{2\pi@} x^@{(x-1/2)@} \exp(-x)) 541 = (1 + (1/12x) + ...) for x \to \infty 542 543and is a useful suggestion of Temme. 544EOF 545${RT} D_D >> gsl_sf.cc 546 547## Deprecated naming scheme 548export octave_name=gammastar 549export funcname=gsl_sf_gammastar_e 550${RT} D_D >> gsl_sf.cc 551 552###################################################################### 553 554export octave_name=gsl_sf_gammainv 555export funcname=gsl_sf_gammainv_e 556cat << \EOF > docstring.txt 557Computes the reciprocal of the gamma function, 1/\Gamma(x) using the real Lanczos method. 558EOF 559${RT} D_D >> gsl_sf.cc 560 561## Deprecated naming scheme 562export octave_name=gammainv_gsl 563export funcname=gsl_sf_gammainv_e 564${RT} D_D >> gsl_sf.cc 565 566###################################################################### 567 568export octave_name=gsl_sf_lambert_W0 569export funcname=gsl_sf_lambert_W0_e 570cat << \EOF > docstring.txt 571These compute the principal branch of the Lambert W function, W_0(x). 572 573Lambert\'s W functions, W(x), are defined to be solutions of the 574export octave_name=gammastar 575export funcname=gsl_sf_gammastar_e 576equation W(x) \exp(W(x)) = x. This function has multiple branches 577for x < 0; however, it has only two real-valued branches. 578We define W_0(x) to be the principal branch, where W > -1 for x < 0, 579and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. 580EOF 581${RT} D_D >> gsl_sf.cc 582 583## Deprecated naming scheme 584export octave_name=lambert_W0 585export funcname=gsl_sf_lambert_W0_e 586${RT} D_D >> gsl_sf.cc 587 588###################################################################### 589 590export octave_name=gsl_sf_lambert_Wm1 591export funcname=gsl_sf_lambert_Wm1_e 592cat << \EOF > docstring.txt 593These compute the secondary real-valued branch of the Lambert 594W function, W_@{-1@}(x). 595 596Lambert\'s W functions, W(x), are defined to be solutions of the 597equation W(x) \exp(W(x)) = x. This function has multiple branches 598for x < 0; however, it has only two real-valued branches. 599We define W_0(x) to be the principal branch, where W > -1 for x < 0, 600and W_@{-1@}(x) to be the other real branch, where W < -1 for x < 0. 601EOF 602${RT} D_D >> gsl_sf.cc 603 604## Deprecated naming scheme 605export octave_name=lambert_Wm1 606export funcname=gsl_sf_lambert_Wm1_e 607${RT} D_D >> gsl_sf.cc 608 609###################################################################### 610 611export octave_name=gsl_sf_log_1plusx 612export funcname=gsl_sf_log_1plusx_e 613cat << \EOF > docstring.txt 614Computes \log(1 + x) for x > -1 using an algorithm that 615is accurate for small x. 616EOF 617${RT} D_D >> gsl_sf.cc 618 619## Deprecated naming scheme 620export octave_name=log_1plusx 621export funcname=gsl_sf_log_1plusx_e 622${RT} D_D >> gsl_sf.cc 623 624###################################################################### 625 626export octave_name=gsl_sf_log_1plusx_mx 627export funcname=gsl_sf_log_1plusx_mx_e 628cat << \EOF > docstring.txt 629Computes \log(1 + x) - x for x > -1 using an algorithm 630that is accurate for small x. 631EOF 632${RT} D_D >> gsl_sf.cc 633 634## Deprecated naming scheme 635export octave_name=log_1plusx_mx 636export funcname=gsl_sf_log_1plusx_mx_e 637${RT} D_D >> gsl_sf.cc 638 639###################################################################### 640 641export octave_name=gsl_sf_psi 642export funcname=gsl_sf_psi_e 643cat << \EOF > docstring.txt 644Computes the digamma function \psi(x) for general x, 645x \ne 0. 646EOF 647${RT} D_D >> gsl_sf.cc 648 649## Deprecated naming scheme 650export octave_name=psi 651export funcname=gsl_sf_psi_e 652${RT} D_D >> gsl_sf.cc 653 654###################################################################### 655 656export octave_name=gsl_sf_psi_1piy 657export funcname=gsl_sf_psi_1piy_e 658cat << \EOF > docstring.txt 659Computes the real part of the digamma function on 660the line 1+i y, Re[\psi(1 + i y)]. 661EOF 662${RT} D_D >> gsl_sf.cc 663 664## Deprecated naming scheme 665export octave_name=psi_1piy 666export funcname=gsl_sf_psi_1piy_e 667${RT} D_D >> gsl_sf.cc 668 669###################################################################### 670 671export octave_name=gsl_sf_synchrotron_1 672export funcname=gsl_sf_synchrotron_1_e 673cat << \EOF > docstring.txt 674Computes the first synchrotron function 675x \int_x^\infty dt K_@{5/3@}(t) for x >= 0. 676EOF 677${RT} D_D >> gsl_sf.cc 678 679## Deprecated naming scheme 680export octave_name=synchrotron_1 681export funcname=gsl_sf_synchrotron_1_e 682${RT} D_D >> gsl_sf.cc 683 684###################################################################### 685 686export octave_name=gsl_sf_synchrotron_2 687export funcname=gsl_sf_synchrotron_2_e 688cat << \EOF > docstring.txt 689Computes the second synchrotron function 690x K_@{2/3@}(x) for x >= 0. 691EOF 692${RT} D_D >> gsl_sf.cc 693 694## Deprecated naming scheme 695export octave_name=synchrotron_2 696export funcname=gsl_sf_synchrotron_2_e 697${RT} D_D >> gsl_sf.cc 698 699###################################################################### 700 701export octave_name=gsl_sf_transport_2 702export funcname=gsl_sf_transport_2_e 703cat << \EOF > docstring.txt 704Computes the transport function J(2,x). 705 706The transport functions J(n,x) are defined by the integral 707representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. 708EOF 709${RT} D_D >> gsl_sf.cc 710 711## Deprecated naming scheme 712export octave_name=transport_2 713export funcname=gsl_sf_transport_2_e 714${RT} D_D >> gsl_sf.cc 715 716###################################################################### 717 718export octave_name=gsl_sf_transport_3 719export funcname=gsl_sf_transport_3_e 720cat << \EOF > docstring.txt 721Computes the transport function J(3,x). 722 723The transport functions J(n,x) are defined by the integral 724representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. 725EOF 726${RT} D_D >> gsl_sf.cc 727 728## Deprecated naming scheme 729export octave_name=transport_3 730export funcname=gsl_sf_transport_3_e 731${RT} D_D >> gsl_sf.cc 732 733###################################################################### 734 735export octave_name=gsl_sf_transport_4 736export funcname=gsl_sf_transport_4_e 737cat << \EOF > docstring.txt 738Computes the transport function J(4,x). 739 740The transport functions J(n,x) are defined by the integral 741representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. 742EOF 743${RT} D_D >> gsl_sf.cc 744 745## Deprecated naming scheme 746export octave_name=transport_4 747export funcname=gsl_sf_transport_4_e 748${RT} D_D >> gsl_sf.cc 749 750###################################################################### 751 752export octave_name=gsl_sf_transport_5 753export funcname=gsl_sf_transport_5_e 754cat << \EOF > docstring.txt 755Computes the transport function J(5,x). 756 757The transport functions J(n,x) are defined by the integral 758representations J(n,x) := \int_0^x dt t^n e^t /(e^t - 1)^2. 759EOF 760${RT} D_D >> gsl_sf.cc 761 762## Deprecated naming scheme 763export octave_name=transport_5 764export funcname=gsl_sf_transport_5_e 765${RT} D_D >> gsl_sf.cc 766 767###################################################################### 768 769export octave_name=gsl_sf_sinc 770export funcname=gsl_sf_sinc_e 771cat << \EOF > docstring.txt 772Computes \sinc(x) = \sin(\pi x) / (\pi x) for any value of x. 773EOF 774${RT} D_D >> gsl_sf.cc 775 776## Deprecated naming scheme 777export octave_name=sinc_gsl 778export funcname=gsl_sf_sinc_e 779${RT} D_D >> gsl_sf.cc 780 781###################################################################### 782 783export octave_name=gsl_sf_lnsinh 784export funcname=gsl_sf_lnsinh_e 785cat << \EOF > docstring.txt 786Computes \log(\sinh(x)) for x > 0. 787EOF 788${RT} D_D >> gsl_sf.cc 789 790## Deprecated naming scheme 791export octave_name=lnsinh 792export funcname=gsl_sf_lnsinh_e 793${RT} D_D >> gsl_sf.cc 794 795###################################################################### 796 797export octave_name=gsl_sf_lncosh 798export funcname=gsl_sf_lncosh_e 799cat << \EOF > docstring.txt 800Computes \log(\cosh(x)) for any x. 801EOF 802${RT} D_D >> gsl_sf.cc 803 804## Deprecated naming scheme 805export octave_name=lncosh 806export funcname=gsl_sf_lncosh_e 807${RT} D_D >> gsl_sf.cc 808 809 810# (int, double) to double ############################################ 811 812export octave_name=gsl_sf_bessel_Jn 813export funcname=gsl_sf_bessel_Jn_e 814cat << \EOF > docstring.txt 815Computes the regular cylindrical Bessel function of 816order n, J_n(x). 817EOF 818${RT} ID_D >> gsl_sf.cc 819 820## Deprecated naming scheme 821export octave_name=bessel_Jn 822export funcname=gsl_sf_bessel_Jn_e 823${RT} ID_D >> gsl_sf.cc 824 825###################################################################### 826 827export octave_name=gsl_sf_bessel_Yn 828export funcname=gsl_sf_bessel_Yn_e 829cat << \EOF > docstring.txt 830Computes the irregular cylindrical Bessel function of 831order n, Y_n(x), for x>0. 832EOF 833${RT} ID_D >> gsl_sf.cc 834 835## Deprecated naming scheme 836export octave_name=bessel_Yn 837export funcname=gsl_sf_bessel_Yn_e 838${RT} ID_D >> gsl_sf.cc 839 840###################################################################### 841 842export octave_name=gsl_sf_bessel_In 843export funcname=gsl_sf_bessel_In_e 844cat << \EOF > docstring.txt 845Computes the regular modified cylindrical Bessel 846function of order n, I_n(x). 847EOF 848${RT} ID_D >> gsl_sf.cc 849 850## Deprecated naming scheme 851export octave_name=bessel_In 852export funcname=gsl_sf_bessel_In_e 853${RT} ID_D >> gsl_sf.cc 854 855###################################################################### 856 857export octave_name=gsl_sf_bessel_In_scaled 858export funcname=gsl_sf_bessel_In_scaled_e 859cat << \EOF > docstring.txt 860Computes the scaled regular modified cylindrical Bessel 861function of order n, \exp(-|x|) I_n(x) 862EOF 863${RT} ID_D >> gsl_sf.cc 864 865## Deprecated naming scheme 866export octave_name=bessel_In_scaled 867export funcname=gsl_sf_bessel_In_scaled_e 868${RT} ID_D >> gsl_sf.cc 869 870###################################################################### 871 872export octave_name=gsl_sf_bessel_Kn 873export funcname=gsl_sf_bessel_Kn_e 874cat << \EOF > docstring.txt 875Computes the irregular modified cylindrical Bessel 876function of order n, K_n(x), for x > 0. 877EOF 878${RT} ID_D >> gsl_sf.cc 879 880## Deprecated naming scheme 881export octave_name=bessel_Kn 882export funcname=gsl_sf_bessel_Kn_e 883${RT} ID_D >> gsl_sf.cc 884 885###################################################################### 886 887export octave_name=gsl_sf_bessel_Kn_scaled 888export funcname=gsl_sf_bessel_Kn_scaled_e 889cat << \EOF > docstring.txt 890 891EOF 892${RT} ID_D >> gsl_sf.cc 893 894## Deprecated naming scheme 895export octave_name=bessel_Kn_scaled 896export funcname=gsl_sf_bessel_Kn_scaled_e 897${RT} ID_D >> gsl_sf.cc 898 899###################################################################### 900 901export octave_name=gsl_sf_bessel_jl 902export funcname=gsl_sf_bessel_jl_e 903cat << \EOF > docstring.txt 904Computes the regular spherical Bessel function of 905order l, j_l(x), for l >= 0 and x >= 0. 906EOF 907${RT} ID_D >> gsl_sf.cc 908 909## Deprecated naming scheme 910export octave_name=bessel_jl 911export funcname=gsl_sf_bessel_jl_e 912${RT} ID_D >> gsl_sf.cc 913 914###################################################################### 915 916export octave_name=gsl_sf_bessel_yl 917export funcname=gsl_sf_bessel_yl_e 918cat << \EOF > docstring.txt 919Computes the irregular spherical Bessel function of 920order l, y_l(x), for l >= 0. 921EOF 922${RT} ID_D >> gsl_sf.cc 923 924## Deprecated naming scheme 925export octave_name=bessel_yl 926export funcname=gsl_sf_bessel_yl_e 927${RT} ID_D >> gsl_sf.cc 928 929###################################################################### 930 931export octave_name=gsl_sf_bessel_il_scaled 932export funcname=gsl_sf_bessel_il_scaled_e 933cat << \EOF > docstring.txt 934Computes the scaled regular modified spherical Bessel 935function of order l, \exp(-|x|) i_l(x) 936EOF 937${RT} ID_D >> gsl_sf.cc 938 939## Deprecated naming scheme 940export octave_name=bessel_il_scaled 941export funcname=gsl_sf_bessel_il_scaled_e 942${RT} ID_D >> gsl_sf.cc 943 944###################################################################### 945 946export octave_name=gsl_sf_bessel_kl_scaled 947export funcname=gsl_sf_bessel_kl_scaled_e 948cat << \EOF > docstring.txt 949Computes the scaled irregular modified spherical Bessel 950function of order l, \exp(x) k_l(x), for x>0. 951EOF 952${RT} ID_D >> gsl_sf.cc 953 954## Deprecated naming scheme 955export octave_name=bessel_kl_scaled 956export funcname=gsl_sf_bessel_kl_scaled_e 957${RT} ID_D >> gsl_sf.cc 958 959###################################################################### 960 961export octave_name=gsl_sf_exprel_n 962export funcname=gsl_sf_exprel_n_e 963cat << \EOF > docstring.txt 964Computes the N-relative exponential, which is the n-th 965generalization of the functions gsl_sf_exprel and gsl_sf_exprel2. The 966N-relative exponential is given by, 967 968exprel_N(x) = N!/x^N (\exp(x) - \sum_@{k=0@}^@{N-1@} x^k/k!) 969 = 1 + x/(N+1) + x^2/((N+1)(N+2)) + ... 970 = 1F1 (1,1+N,x) 971EOF 972${RT} ID_D >> gsl_sf.cc 973 974## Deprecated naming scheme 975export octave_name=exprel_n 976export funcname=gsl_sf_exprel_n_e 977${RT} ID_D >> gsl_sf.cc 978 979###################################################################### 980 981export octave_name=gsl_sf_fermi_dirac_int 982export funcname=gsl_sf_fermi_dirac_int_e 983cat << \EOF > docstring.txt 984Computes the complete Fermi-Dirac integral with an 985integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j 986/(\exp(t-x)+1)). 987EOF 988${RT} ID_D >> gsl_sf.cc 989 990## Deprecated naming scheme 991export octave_name=fermi_dirac_int 992export funcname=gsl_sf_fermi_dirac_int_e 993${RT} ID_D >> gsl_sf.cc 994 995###################################################################### 996 997export octave_name=gsl_sf_taylorcoeff 998export funcname=gsl_sf_taylorcoeff_e 999cat << \EOF > docstring.txt 1000Computes the Taylor coefficient x^n / n! 1001for x >= 0, n >= 0. 1002EOF 1003${RT} ID_D >> gsl_sf.cc 1004 1005## Deprecated naming scheme 1006export octave_name=taylorcoeff 1007export funcname=gsl_sf_taylorcoeff_e 1008${RT} ID_D >> gsl_sf.cc 1009 1010###################################################################### 1011 1012export octave_name=gsl_sf_legendre_Pl 1013export funcname=gsl_sf_legendre_Pl_e 1014cat << \EOF > docstring.txt 1015These functions evaluate the Legendre polynomial P_l(x) for a specific 1016value of l, x subject to l >= 0, |x| <= 1 1017EOF 1018${RT} ID_D >> gsl_sf.cc 1019 1020## Deprecated naming scheme 1021export octave_name=legendre_Pl 1022export funcname=gsl_sf_legendre_Pl_e 1023${RT} ID_D >> gsl_sf.cc 1024 1025###################################################################### 1026 1027export octave_name=gsl_sf_legendre_Ql 1028export funcname=gsl_sf_legendre_Ql_e 1029cat << \EOF > docstring.txt 1030Computes the Legendre function Q_l(x) for x > -1, x != 1 1031and l >= 0. 1032EOF 1033${RT} ID_D >> gsl_sf.cc 1034 1035## Deprecated naming scheme 1036export octave_name=legendre_Ql 1037export funcname=gsl_sf_legendre_Ql_e 1038${RT} ID_D >> gsl_sf.cc 1039 1040###################################################################### 1041 1042export octave_name=gsl_sf_mathieu_a 1043export funcname=gsl_sf_mathieu_a_e 1044cat << \EOF > docstring.txt 1045Computes the characteristic values a_n(q) of the 1046Mathieu function ce_n(q,x). 1047EOF 1048${RT} ID_D >> gsl_sf.cc 1049 1050###################################################################### 1051 1052export octave_name=gsl_sf_mathieu_b 1053export funcname=gsl_sf_mathieu_b_e 1054cat << \EOF > docstring.txt 1055Computes the characteristic values b_n(q) of the 1056Mathieu function se_n(q,x). 1057EOF 1058${RT} ID_D >> gsl_sf.cc 1059 1060###################################################################### 1061 1062export octave_name=gsl_sf_psi_n 1063export funcname=gsl_sf_psi_n_e 1064cat << \EOF > docstring.txt 1065Computes the polygamma function \psi^@{(m)@}(x) 1066for m >= 0, x > 0. 1067EOF 1068${RT} ID_D >> gsl_sf.cc 1069 1070## Deprecated naming scheme 1071export octave_name=psi_n 1072export funcname=gsl_sf_psi_n_e 1073${RT} ID_D >> gsl_sf.cc 1074 1075 1076# (double, double) to double ######################################### 1077 1078export octave_name=gsl_sf_bessel_Jnu 1079export funcname=gsl_sf_bessel_Jnu_e 1080cat << \EOF > docstring.txt 1081Computes the regular cylindrical Bessel function of 1082fractional order nu, J_\nu(x). 1083EOF 1084${RT} DD_D >> gsl_sf.cc 1085 1086## Deprecated naming scheme 1087export octave_name=bessel_Jnu 1088export funcname=gsl_sf_bessel_Jnu_e 1089${RT} DD_D >> gsl_sf.cc 1090 1091###################################################################### 1092 1093export octave_name=gsl_sf_bessel_Ynu 1094export funcname=gsl_sf_bessel_Ynu_e 1095cat << \EOF > docstring.txt 1096Computes the irregular cylindrical Bessel function of 1097fractional order nu, Y_\nu(x). 1098EOF 1099${RT} DD_D >> gsl_sf.cc 1100 1101## Deprecated naming scheme 1102export octave_name=bessel_Ynu 1103export funcname=gsl_sf_bessel_Ynu_e 1104${RT} DD_D >> gsl_sf.cc 1105 1106###################################################################### 1107 1108export octave_name=gsl_sf_bessel_Inu 1109export funcname=gsl_sf_bessel_Inu_e 1110cat << \EOF > docstring.txt 1111Computes the regular modified Bessel function of 1112fractional order nu, I_\nu(x) for x>0, \nu>0. 1113EOF 1114${RT} DD_D >> gsl_sf.cc 1115 1116## Deprecated naming scheme 1117export octave_name=bessel_Inu 1118export funcname=gsl_sf_bessel_Inu_e 1119${RT} DD_D >> gsl_sf.cc 1120 1121###################################################################### 1122 1123export octave_name=gsl_sf_bessel_Inu_scaled 1124export funcname=gsl_sf_bessel_Inu_scaled_e 1125cat << \EOF > docstring.txt 1126Computes the scaled regular modified Bessel function of 1127fractional order nu, \exp(-|x|)I_\nu(x) for x>0, \nu>0. 1128EOF 1129${RT} DD_D >> gsl_sf.cc 1130 1131## Deprecated naming scheme 1132export octave_name=bessel_Inu_scaled 1133export funcname=gsl_sf_bessel_Inu_scaled_e 1134${RT} DD_D >> gsl_sf.cc 1135 1136###################################################################### 1137 1138export octave_name=gsl_sf_bessel_Knu 1139export funcname=gsl_sf_bessel_Knu_e 1140cat << \EOF > docstring.txt 1141Computes the irregular modified Bessel function of 1142fractional order nu, K_\nu(x) for x>0, \nu>0. 1143EOF 1144${RT} DD_D >> gsl_sf.cc 1145 1146## Deprecated naming scheme 1147export octave_name=bessel_Knu 1148export funcname=gsl_sf_bessel_Knu_e 1149${RT} DD_D >> gsl_sf.cc 1150 1151###################################################################### 1152 1153export octave_name=gsl_sf_bessel_lnKnu 1154export funcname=gsl_sf_bessel_lnKnu_e 1155cat << \EOF > docstring.txt 1156Computes the logarithm of the irregular modified Bessel 1157function of fractional order nu, \ln(K_\nu(x)) for x>0, \nu>0. 1158EOF 1159${RT} DD_D >> gsl_sf.cc 1160 1161## Deprecated naming scheme 1162export octave_name=bessel_lnKnu 1163export funcname=gsl_sf_bessel_lnKnu_e 1164${RT} DD_D >> gsl_sf.cc 1165 1166###################################################################### 1167 1168export octave_name=gsl_sf_bessel_Knu_scaled 1169export funcname=gsl_sf_bessel_Knu_scaled_e 1170cat << \EOF > docstring.txt 1171Computes the scaled irregular modified Bessel function 1172of fractional order nu, \exp(+|x|) K_\nu(x) for x>0, \nu>0. 1173EOF 1174${RT} DD_D >> gsl_sf.cc 1175 1176## Deprecated naming scheme 1177export octave_name=bessel_Knu_scaled 1178export funcname=gsl_sf_bessel_Knu_scaled_e 1179${RT} DD_D >> gsl_sf.cc 1180 1181###################################################################### 1182 1183export octave_name=gsl_sf_exp_mult 1184export funcname=gsl_sf_exp_mult_e 1185cat << \EOF > docstring.txt 1186These routines exponentiate x and multiply by the factor y to return 1187the product y \exp(x). 1188EOF 1189${RT} DD_D >> gsl_sf.cc 1190 1191## Deprecated naming scheme 1192export octave_name=exp_mult 1193export funcname=gsl_sf_exp_mult_e 1194${RT} DD_D >> gsl_sf.cc 1195 1196###################################################################### 1197 1198export octave_name=gsl_sf_fermi_dirac_inc_0 1199export funcname=gsl_sf_fermi_dirac_inc_0_e 1200cat << \EOF > docstring.txt 1201Computes the incomplete Fermi-Dirac integral with an 1202index of zero, F_0(x,b) = \ln(1 + e^@{b-x@}) - (b-x). 1203EOF 1204${RT} DD_D >> gsl_sf.cc 1205 1206## Deprecated naming scheme 1207export octave_name=fermi_dirac_inc_0 1208export funcname=gsl_sf_fermi_dirac_inc_0_e 1209${RT} DD_D >> gsl_sf.cc 1210 1211###################################################################### 1212 1213export octave_name=gsl_sf_poch 1214export funcname=gsl_sf_poch_e 1215cat << \EOF > docstring.txt 1216Computes the Pochhammer symbol 1217 1218(a)_x := \Gamma(a + x)/\Gamma(a), 1219 1220subject to a and a+x not being negative integers. The Pochhammer 1221symbol is also known as the Apell symbol. 1222EOF 1223${RT} DD_D >> gsl_sf.cc 1224 1225## Deprecated naming scheme 1226export octave_name=poch 1227export funcname=gsl_sf_poch_e 1228${RT} DD_D >> gsl_sf.cc 1229 1230###################################################################### 1231 1232export octave_name=gsl_sf_lnpoch 1233export funcname=gsl_sf_lnpoch_e 1234cat << \EOF > docstring.txt 1235Computes the logarithm of the Pochhammer symbol, 1236\log((a)_x) = \log(\Gamma(a + x)/\Gamma(a)) for a > 0, a+x > 0. 1237EOF 1238${RT} DD_D >> gsl_sf.cc 1239 1240## Deprecated naming scheme 1241export octave_name=lnpoch 1242export funcname=gsl_sf_lnpoch_e 1243${RT} DD_D >> gsl_sf.cc 1244 1245###################################################################### 1246 1247export octave_name=gsl_sf_pochrel 1248export funcname=gsl_sf_pochrel_e 1249cat << \EOF > docstring.txt 1250Computes the relative Pochhammer symbol ((a,x) - 1)/x 1251where (a,x) = (a)_x := \Gamma(a + x)/\Gamma(a). 1252EOF 1253${RT} DD_D >> gsl_sf.cc 1254 1255## Deprecated naming scheme 1256export octave_name=pochrel 1257export funcname=gsl_sf_pochrel_e 1258${RT} DD_D >> gsl_sf.cc 1259 1260###################################################################### 1261 1262export octave_name=gsl_sf_gamma_inc_Q 1263export funcname=gsl_sf_gamma_inc_Q_e 1264cat << \EOF > docstring.txt 1265Computes the normalized incomplete Gamma Function 1266Q(a,x) = 1/\Gamma(a) \int_x\infty dt t^@{a-1@} \exp(-t) for a > 0, x >= 0. 1267EOF 1268${RT} DD_D >> gsl_sf.cc 1269 1270## Deprecated naming scheme 1271export octave_name=gamma_inc_Q 1272export funcname=gsl_sf_gamma_inc_Q_e 1273${RT} DD_D >> gsl_sf.cc 1274 1275###################################################################### 1276 1277export octave_name=gsl_sf_gamma_inc_P 1278export funcname=gsl_sf_gamma_inc_P_e 1279cat << \EOF > docstring.txt 1280Computes the complementary normalized incomplete Gamma 1281Function P(a,x) = 1/\Gamma(a) \int_0^x dt t^@{a-1@} \exp(-t) 1282for a > 0, x >= 0. 1283EOF 1284${RT} DD_D >> gsl_sf.cc 1285 1286## Deprecated naming scheme 1287export octave_name=gamma_inc_P 1288export funcname=gsl_sf_gamma_inc_P_e 1289${RT} DD_D >> gsl_sf.cc 1290 1291###################################################################### 1292 1293export octave_name=gsl_sf_gamma_inc 1294export funcname=gsl_sf_gamma_inc_e 1295cat << \EOF > docstring.txt 1296These functions compute the incomplete Gamma Function the 1297normalization factor included in the previously defined functions: 1298\Gamma(a,x) = \int_x\infty dt t^@{a-1@} \exp(-t) for a real and x >= 0. 1299EOF 1300${RT} DD_D >> gsl_sf.cc 1301 1302## Deprecated naming scheme 1303export octave_name=gamma_inc 1304export funcname=gsl_sf_gamma_inc_e 1305${RT} DD_D >> gsl_sf.cc 1306 1307###################################################################### 1308 1309export octave_name=gsl_sf_beta 1310export funcname=gsl_sf_beta_e 1311cat << \EOF > docstring.txt 1312Computes the Beta Function, 1313B(a,b) = \Gamma(a)\Gamma(b)/\Gamma(a+b) for a > 0, b > 0. 1314EOF 1315${RT} DD_D >> gsl_sf.cc 1316 1317## Deprecated naming scheme 1318export octave_name=beta_gsl 1319export funcname=gsl_sf_beta_e 1320${RT} DD_D >> gsl_sf.cc 1321 1322###################################################################### 1323 1324export octave_name=gsl_sf_lnbeta 1325export funcname=gsl_sf_lnbeta_e 1326cat << \EOF > docstring.txt 1327Computes the logarithm of the Beta Function, 1328\log(B(a,b)) for a > 0, b > 0. 1329EOF 1330${RT} DD_D >> gsl_sf.cc 1331 1332## Deprecated naming scheme 1333export octave_name=lnbeta 1334export funcname=gsl_sf_lnbeta_e 1335${RT} DD_D >> gsl_sf.cc 1336 1337###################################################################### 1338 1339export octave_name=gsl_sf_hyperg_0F1 1340export funcname=gsl_sf_hyperg_0F1_e 1341cat << \EOF > docstring.txt 1342Computes the hypergeometric function 0F1(c,x). 1343EOF 1344${RT} DD_D >> gsl_sf.cc 1345 1346## Deprecated naming scheme 1347export octave_name=hyperg_0F1 1348export funcname=gsl_sf_hyperg_0F1_e 1349${RT} DD_D >> gsl_sf.cc 1350 1351###################################################################### 1352 1353export octave_name=gsl_sf_conicalP_half 1354export funcname=gsl_sf_conicalP_half_e 1355cat << \EOF > docstring.txt 1356Computes the irregular Spherical Conical Function 1357P^@{1/2@}_@{-1/2 + i \lambda@}(x) for x > -1. 1358EOF 1359${RT} DD_D >> gsl_sf.cc 1360 1361## Deprecated naming scheme 1362export octave_name=conicalP_half 1363export funcname=gsl_sf_conicalP_half_e 1364${RT} DD_D >> gsl_sf.cc 1365 1366###################################################################### 1367 1368export octave_name=gsl_sf_conicalP_mhalf 1369export funcname=gsl_sf_conicalP_mhalf_e 1370cat << \EOF > docstring.txt 1371Computes the regular Spherical Conical Function 1372P^@{-1/2@}_@{-1/2 + i \lambda@}(x) for x > -1. 1373EOF 1374${RT} DD_D >> gsl_sf.cc 1375 1376## Deprecated naming scheme 1377export octave_name=conicalP_mhalf 1378export funcname=gsl_sf_conicalP_mhalf_e 1379${RT} DD_D >> gsl_sf.cc 1380 1381###################################################################### 1382 1383export octave_name=gsl_sf_conicalP_0 1384export funcname=gsl_sf_conicalP_0_e 1385cat << \EOF > docstring.txt 1386Computes the conical function P^0_@{-1/2 + i \lambda@}(x) 1387for x > -1. 1388EOF 1389${RT} DD_D >> gsl_sf.cc 1390 1391## Deprecated naming scheme 1392export octave_name=conicalP_0 1393export funcname=gsl_sf_conicalP_0_e 1394${RT} DD_D >> gsl_sf.cc 1395 1396###################################################################### 1397 1398export octave_name=gsl_sf_conicalP_1 1399export funcname=gsl_sf_conicalP_1_e 1400cat << \EOF > docstring.txt 1401Computes the conical function P^1_@{-1/2 + i \lambda@}(x) 1402for x > -1. 1403EOF 1404${RT} DD_D >> gsl_sf.cc 1405 1406## Deprecated naming scheme 1407export octave_name=conicalP_1 1408export funcname=gsl_sf_conicalP_1_e 1409${RT} DD_D >> gsl_sf.cc 1410 1411 1412# (double, mode) to double ########################################### 1413 1414export octave_name=gsl_sf_airy_Ai 1415export funcname=gsl_sf_airy_Ai_e 1416cat << \EOF > docstring.txt 1417Computes the Airy function Ai(x) with an accuracy 1418specified by mode. 1419EOF 1420${RT} DM_D >> gsl_sf.cc 1421 1422## Deprecated naming scheme 1423export octave_name=airy_Ai 1424export funcname=gsl_sf_airy_Ai_e 1425${RT} DM_D >> gsl_sf.cc 1426 1427###################################################################### 1428 1429export octave_name=gsl_sf_airy_Bi 1430export funcname=gsl_sf_airy_Bi_e 1431cat << \EOF > docstring.txt 1432Computes the Airy function Bi(x) with an accuracy 1433specified by mode. 1434EOF 1435${RT} DM_D >> gsl_sf.cc 1436 1437## Deprecated naming scheme 1438export octave_name=airy_Bi 1439export funcname=gsl_sf_airy_Bi_e 1440${RT} DM_D >> gsl_sf.cc 1441 1442###################################################################### 1443 1444export octave_name=gsl_sf_airy_Ai_scaled 1445export funcname=gsl_sf_airy_Ai_scaled_e 1446cat << \EOF > docstring.txt 1447Computes a scaled version of the Airy function 1448S_A(x) Ai(x). For x>0 the scaling factor S_A(x) is \exp(+(2/3) x^(3/2)), and 1449is 1 for x<0. 1450EOF 1451${RT} DM_D >> gsl_sf.cc 1452 1453## Deprecated naming scheme 1454export octave_name=airy_Ai_scaled 1455export funcname=gsl_sf_airy_Ai_scaled_e 1456${RT} DM_D >> gsl_sf.cc 1457 1458###################################################################### 1459 1460export octave_name=gsl_sf_airy_Bi_scaled 1461export funcname=gsl_sf_airy_Bi_scaled_e 1462cat << \EOF > docstring.txt 1463Computes a scaled version of the Airy function 1464S_B(x) Bi(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and 1465is 1 for x<0. 1466EOF 1467${RT} DM_D >> gsl_sf.cc 1468 1469## Deprecated naming scheme 1470export octave_name=airy_Bi_scaled 1471export funcname=gsl_sf_airy_Bi_scaled_e 1472${RT} DM_D >> gsl_sf.cc 1473 1474###################################################################### 1475 1476export octave_name=gsl_sf_airy_Ai_deriv 1477export funcname=gsl_sf_airy_Ai_deriv_e 1478cat << \EOF > docstring.txt 1479Computes the Airy function derivative Ai'(x) with an 1480accuracy specified by mode. 1481EOF 1482${RT} DM_D >> gsl_sf.cc 1483 1484## Deprecated naming scheme 1485export octave_name=airy_Ai_deriv 1486export funcname=gsl_sf_airy_Ai_deriv_e 1487${RT} DM_D >> gsl_sf.cc 1488 1489###################################################################### 1490 1491export octave_name=gsl_sf_airy_Bi_deriv 1492export funcname=gsl_sf_airy_Bi_deriv_e 1493cat << \EOF > docstring.txt 1494Computes the Airy function derivative Bi'(x) with an 1495accuracy specified by mode. 1496EOF 1497${RT} DM_D >> gsl_sf.cc 1498 1499## Deprecated naming scheme 1500export octave_name=airy_Bi_deriv 1501export funcname=gsl_sf_airy_Bi_deriv_e 1502${RT} DM_D >> gsl_sf.cc 1503 1504###################################################################### 1505 1506export octave_name=gsl_sf_airy_Ai_deriv_scaled 1507export funcname=gsl_sf_airy_Ai_deriv_scaled_e 1508cat << \EOF > docstring.txt 1509Computes the derivative of the scaled Airy function 1510S_A(x) Ai(x). 1511EOF 1512${RT} DM_D >> gsl_sf.cc 1513 1514## Deprecated naming scheme 1515export octave_name=airy_Ai_deriv_scaled 1516export funcname=gsl_sf_airy_Ai_deriv_scaled_e 1517${RT} DM_D >> gsl_sf.cc 1518 1519###################################################################### 1520 1521export octave_name=gsl_sf_airy_Bi_deriv_scaled 1522export funcname=gsl_sf_airy_Bi_deriv_scaled_e 1523cat << \EOF > docstring.txt 1524Computes the derivative of the scaled Airy function 1525S_B(x) Bi(x). 1526EOF 1527${RT} DM_D >> gsl_sf.cc 1528 1529## Deprecated naming scheme 1530export octave_name=airy_Bi_deriv_scaled 1531export funcname=gsl_sf_airy_Bi_deriv_scaled_e 1532${RT} DM_D >> gsl_sf.cc 1533 1534###################################################################### 1535 1536export octave_name=gsl_sf_ellint_Kcomp 1537export funcname=gsl_sf_ellint_Kcomp_e 1538cat << \EOF > docstring.txt 1539Computes the complete elliptic integral K(k) 1540@tex 1541\beforedisplay 1542$$ 1543\eqalign{ 1544K(k) &= \int_0^{\pi/2} {dt \over \sqrt{(1 - k^2 \sin^2(t))}} \cr 1545} 1546$$ 1547\afterdisplay 1548See also: 1549@end tex 1550@ifinfo 1551@group 1552@example 1553 pi 1554 --- 1555 2 1556 / 1557 | 1 1558 ellint_Kcomp(k) = | ------------------- dt 1559 | 2 2 1560 / sqrt(1 - k sin (t)) 1561 0 1562 1563@end example 1564@end group 1565@end ifinfo 1566@ifhtml 1567@group 1568@example 1569 pi 1570 --- 1571 2 1572 / 1573 | 1 1574 ellint_Kcomp(k) = | ------------------- dt 1575 | 2 2 1576 / sqrt(1 - k sin (t)) 1577 0 1578 1579@end example 1580@end group 1581@end ifhtml 1582 1583@seealso{ellipj, ellipke} 1584 1585The notation used here is based on Carlson, @cite{Numerische 1586Mathematik} 33 (1979) and differs slightly from that used by 1587Abramowitz & Stegun, where the functions are given in terms of the 1588parameter @math{m = k^2}. 1589 1590EOF 1591${RT} DM_D >> gsl_sf.cc 1592 1593## Deprecated naming scheme 1594export octave_name=ellint_Kcomp 1595export funcname=gsl_sf_ellint_Kcomp_e 1596${RT} DM_D >> gsl_sf.cc 1597 1598###################################################################### 1599 1600export octave_name=gsl_sf_ellint_Ecomp 1601export funcname=gsl_sf_ellint_Ecomp_e 1602cat << \EOF > docstring.txt 1603Computes the complete elliptic integral E(k) to the 1604accuracy specified by the mode variable mode. 1605 1606@tex 1607\beforedisplay 1608$$ 1609\eqalign{ 1610E(k) &= \int_0^{\pi/2} \sqrt{(1 - k^2 \sin^2(t))} dt \cr 1611} 1612$$ 1613\afterdisplay 1614See also: 1615 1616@end tex 1617@ifinfo 1618@group 1619@example 1620 pi 1621 --- 1622 2 1623 / 1624 | 2 2 1625 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt 1626 | 1627 / 1628 0 1629 1630@end example 1631@end group 1632@end ifinfo 1633@ifhtml 1634@group 1635@example 1636 pi 1637 --- 1638 2 1639 / 1640 | 2 2 1641 ellint_Ecomp(k) = | sqrt(1 - k sin (t)) dt 1642 | 1643 / 1644 0 1645 1646@end example 1647@end group 1648@end ifhtml 1649 1650@seealso{ellipj, ellipke} 1651 1652The notation used here is based on Carlson, @cite{Numerische 1653Mathematik} 33 (1979) and differs slightly from that used by 1654Abramowitz & Stegun, where the functions are given in terms of the 1655parameter @math{m = k^2}. 1656EOF 1657${RT} DM_D >> gsl_sf.cc 1658 1659## Deprecated naming scheme 1660export octave_name=ellint_Ecomp 1661export funcname=gsl_sf_ellint_Ecomp_e 1662${RT} DM_D >> gsl_sf.cc 1663 1664 1665# (double, double, mode) to double ################################### 1666 1667export octave_name=gsl_sf_ellint_E 1668export funcname=gsl_sf_ellint_E_e 1669cat << \EOF > docstring.txt 1670This routine computes the elliptic integral E(\phi,k) to the accuracy 1671specified by the mode variable mode. Note that Abramowitz & Stegun 1672define this function in terms of the parameter m = k^2. 1673EOF 1674${RT} DDM_D >> gsl_sf.cc 1675 1676###################################################################### 1677 1678export octave_name=gsl_sf_ellint_F 1679export funcname=gsl_sf_ellint_F_e 1680cat << \EOF > docstring.txt 1681This routine computes the elliptic integral F(\phi,k) to the accuracy 1682specified by the mode variable mode. Note that Abramowitz & Stegun 1683define this function in terms of the parameter m = k^2. 1684EOF 1685${RT} DDM_D >> gsl_sf.cc 1686 1687###################################################################### 1688 1689export octave_name=gsl_sf_ellint_Pcomp 1690export funcname=gsl_sf_ellint_Pcomp_e 1691cat << \EOF > docstring.txt 1692Computes the complete elliptic integral \Pi(k,n) to the 1693accuracy specified by the mode variable mode. Note that Abramowitz & 1694Stegun define this function in terms of the parameters m = k^2 and 1695\sin^2(\alpha) = k^2, with the change of sign n \to -n. 1696EOF 1697${RT} DDM_D >> gsl_sf.cc 1698 1699###################################################################### 1700 1701export octave_name=gsl_sf_ellint_RC 1702export funcname=gsl_sf_ellint_RC_e 1703cat << \EOF > docstring.txt 1704This routine computes the incomplete elliptic integral RC(x,y) to the 1705accuracy specified by the mode variable mode. 1706EOF 1707${RT} DDM_D >> gsl_sf.cc 1708 1709###################################################################### 1710 1711export octave_name=gsl_sf_ellint_D 1712export funcname=gsl_sf_ellint_D_e 1713cat << \EOF > docstring.txt 1714This function computes the incomplete elliptic integral 1715D(\phi,k) which is defined through the Carlson form 1716RD(x,y,z) by the following relation, 1717 1718D(\phi,k) = (1/3)(\sin(\phi))^3 1719 x RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1). 1720EOF 1721echo "#if GSL_MAJOR_VERSION < 2" >> gsl_sf.cc 1722${RT} DDDM_D >> gsl_sf.cc 1723echo "#else" >> gsl_sf.cc 1724${RT} DDM_D >> gsl_sf.cc 1725echo "#endif" >> gsl_sf.cc 1726 1727 1728# (double, double, double, mode) to double ########################### 1729 1730export octave_name=gsl_sf_ellint_P 1731export funcname=gsl_sf_ellint_P_e 1732cat << \EOF > docstring.txt 1733This routine computes the incomplete elliptic integral \Pi(\phi,k,n) 1734to the accuracy specified by the mode variable mode. Note that 1735Abramowitz & Stegun define this function in terms of the parameters 1736m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n. 1737EOF 1738${RT} DDDM_D >> gsl_sf.cc 1739 1740###################################################################### 1741 1742export octave_name=gsl_sf_ellint_RD 1743export funcname=gsl_sf_ellint_RD_e 1744cat << \EOF > docstring.txt 1745This routine computes the incomplete elliptic integral RD(x,y,z) to the 1746accuracy specified by the mode variable mode. 1747EOF 1748${RT} DDDM_D >> gsl_sf.cc 1749 1750###################################################################### 1751 1752export octave_name=gsl_sf_ellint_RF 1753export funcname=gsl_sf_ellint_RF_e 1754cat << \EOF > docstring.txt 1755This routine computes the incomplete elliptic integral RF(x,y,z) to the 1756accuracy specified by the mode variable mode. 1757EOF 1758${RT} DDDM_D >> gsl_sf.cc 1759 1760 1761# (double, double, double, double, mode) to double ################### 1762 1763export octave_name=gsl_sf_ellint_RJ 1764export funcname=gsl_sf_ellint_RJ_e 1765cat << \EOF > docstring.txt 1766This routine computes the incomplete elliptic integral RJ(x,y,z,p) to the 1767accuracy specified by the mode variable mode. 1768EOF 1769${RT} DDDDM_D >> gsl_sf.cc 1770 1771 1772# int to double ###################################################### 1773 1774export octave_name=gsl_sf_airy_zero_Ai 1775export funcname=gsl_sf_airy_zero_Ai_e 1776cat << \EOF > docstring.txt 1777Computes the location of the s-th zero of the Airy 1778function Ai(x). 1779EOF 1780${RT} I_D >> gsl_sf.cc 1781 1782## Deprecated naming scheme 1783export octave_name=airy_zero_Ai 1784export funcname=gsl_sf_airy_zero_Ai_e 1785${RT} I_D >> gsl_sf.cc 1786 1787###################################################################### 1788 1789export octave_name=gsl_sf_airy_zero_Bi 1790export funcname=gsl_sf_airy_zero_Bi_e 1791cat << \EOF > docstring.txt 1792Computes the location of the s-th zero of the Airy 1793function Bi(x). 1794EOF 1795${RT} I_D >> gsl_sf.cc 1796 1797## Deprecated naming scheme 1798export octave_name=airy_zero_Bi 1799export funcname=gsl_sf_airy_zero_Bi_e 1800${RT} I_D >> gsl_sf.cc 1801 1802###################################################################### 1803 1804export octave_name=gsl_sf_airy_zero_Ai_deriv 1805export funcname=gsl_sf_airy_zero_Ai_deriv_e 1806cat << \EOF > docstring.txt 1807Computes the location of the s-th zero of the Airy 1808function derivative Ai(x). 1809EOF 1810${RT} I_D >> gsl_sf.cc 1811 1812## Deprecated naming scheme 1813export octave_name=airy_zero_Ai_deriv 1814export funcname=gsl_sf_airy_zero_Ai_deriv_e 1815${RT} I_D >> gsl_sf.cc 1816 1817###################################################################### 1818 1819export octave_name=gsl_sf_airy_zero_Bi_deriv 1820export funcname=gsl_sf_airy_zero_Bi_deriv_e 1821cat << \EOF > docstring.txt 1822Computes the location of the s-th zero of the Airy 1823function derivative Bi(x). 1824EOF 1825${RT} I_D >> gsl_sf.cc 1826 1827## Deprecated naming scheme 1828export octave_name=airy_zero_Bi_deriv 1829export funcname=gsl_sf_airy_zero_Bi_deriv_e 1830${RT} I_D >> gsl_sf.cc 1831 1832###################################################################### 1833 1834export octave_name=gsl_sf_bessel_zero_J0 1835export funcname=gsl_sf_bessel_zero_J0_e 1836cat << \EOF > docstring.txt 1837Computes the location of the s-th positive zero of the 1838Bessel function J_0(x). 1839EOF 1840${RT} I_D >> gsl_sf.cc 1841 1842## Deprecated naming scheme 1843export octave_name=bessel_zero_J0 1844export funcname=gsl_sf_bessel_zero_J0_e 1845${RT} I_D >> gsl_sf.cc 1846 1847###################################################################### 1848 1849export octave_name=gsl_sf_bessel_zero_J1 1850export funcname=gsl_sf_bessel_zero_J1_e 1851cat << \EOF > docstring.txt 1852Computes the location of the s-th positive zero of the 1853Bessel function J_1(x). 1854EOF 1855${RT} I_D >> gsl_sf.cc 1856 1857## Deprecated naming scheme 1858export octave_name=bessel_zero_J1 1859export funcname=gsl_sf_bessel_zero_J1_e 1860${RT} I_D >> gsl_sf.cc 1861 1862###################################################################### 1863 1864export octave_name=gsl_sf_psi_1_int 1865export funcname=gsl_sf_psi_1_int_e 1866cat << \EOF > docstring.txt 1867Computes the Trigamma function \psi(n) for positive 1868integer n. 1869EOF 1870${RT} I_D >> gsl_sf.cc 1871 1872## Deprecated naming scheme 1873export octave_name=psi_1_int 1874export funcname=gsl_sf_psi_1_int_e 1875${RT} I_D >> gsl_sf.cc 1876 1877 1878# (int, double, double) to double #################################### 1879 1880export octave_name=gsl_sf_conicalP_cyl_reg 1881export funcname=gsl_sf_conicalP_cyl_reg_e 1882cat << \EOF > docstring.txt 1883Computes the Regular Cylindrical Conical Function 1884@math{P^{-m}_{-1/2 + i \lambda}(x)}, for @math{x > -1}, @math{m} @geq{} @math{-1}. 1885EOF 1886${RT} IDD_D >> gsl_sf.cc 1887 1888###################################################################### 1889 1890export octave_name=gsl_sf_conicalP_sph_reg 1891export funcname=gsl_sf_conicalP_sph_reg_e 1892cat << \EOF > docstring.txt 1893Computes the Regular Spherical Conical Function 1894@math{P^{-1/2-l}_{-1/2 + i \lambda}(x)}, for @math{x > -1}, @math{l} @geq{} @math{-1}. 1895EOF 1896${RT} IDD_D >> gsl_sf.cc 1897 1898###################################################################### 1899 1900export octave_name=gsl_sf_gegenpoly_n 1901export funcname=gsl_sf_gegenpoly_n_e 1902cat << \EOF > docstring.txt 1903These functions evaluate the Gegenbauer polynomial @math{C^{(\lambda)}_n(x)} 1904for n, lambda, x subject to @math{\lambda > -1/2}, @math{n} @geq{} @math{0}. 1905EOF 1906${RT} IDD_D >> gsl_sf.cc 1907 1908###################################################################### 1909 1910export octave_name=gsl_sf_laguerre_n 1911export funcname=gsl_sf_laguerre_n_e 1912cat << \EOF > docstring.txt 1913Computes the generalized Laguerre polynomial @math{L^a_n(x)} for 1914@math{a > -1} and @math{n} @geq{} @math{0}. 1915EOF 1916${RT} IDD_D >> gsl_sf.cc 1917 1918###################################################################### 1919 1920export octave_name=gsl_sf_mathieu_ce 1921export funcname=gsl_sf_mathieu_ce_e 1922cat << \EOF > docstring.txt 1923This routine computes the angular Mathieu function ce_n(q,x). 1924EOF 1925${RT} IDD_D >> gsl_sf.cc 1926 1927###################################################################### 1928 1929export octave_name=gsl_sf_mathieu_se 1930export funcname=gsl_sf_mathieu_se_e 1931cat << \EOF > docstring.txt 1932This routine computes the angular Mathieu function se_n(q,x). 1933EOF 1934${RT} IDD_D >> gsl_sf.cc 1935 1936# (int, int, double) to double 1937 1938###################################################################### 1939 1940export octave_name=gsl_sf_hyperg_U_int 1941export funcname=gsl_sf_hyperg_U_int_e 1942cat << \EOF > docstring.txt 1943Secondary Confluent Hypergoemetric U function A&E 13.1.3 1944m and n are integers. 1945EOF 1946${RT} IID_D >> gsl_sf.cc 1947 1948###################################################################### 1949 1950export octave_name=gsl_sf_hyperg_1F1_int 1951export funcname=gsl_sf_hyperg_1F1_int_e 1952cat << \EOF > docstring.txt 1953Primary Confluent Hypergoemetric U function A&E 13.1.3 1954m and n are integers. 1955EOF 1956${RT} IID_D >> gsl_sf.cc 1957 1958###################################################################### 1959 1960export octave_name=gsl_sf_legendre_Plm 1961export funcname=gsl_sf_legendre_Plm_e 1962cat << \EOF > docstring.txt 1963Computes the associated Legendre polynomial P_l^m(x) 1964for m >= 0, l >= m, |x| <= 1. 1965EOF 1966${RT} IID_D >> gsl_sf.cc 1967 1968## Deprecated naming scheme 1969export octave_name=legendre_Plm 1970export funcname=gsl_sf_legendre_Plm_e 1971${RT} IID_D >> gsl_sf.cc 1972 1973###################################################################### 1974 1975export octave_name=gsl_sf_legendre_sphPlm 1976export funcname=gsl_sf_legendre_sphPlm_e 1977cat << \EOF > docstring.txt 1978Computes the normalized associated Legendre polynomial 1979$\sqrt@{(2l+1)/(4\pi)@} \sqrt@{(l-m)!/(l+m)!@} P_l^m(x)$ suitable for use 1980in spherical harmonics. The parameters must satisfy m >= 0, l >= m, 1981|x| <= 1. Theses routines avoid the overflows that occur for the 1982standard normalization of P_l^m(x). 1983EOF 1984${RT} IID_D >> gsl_sf.cc 1985 1986## Deprecated naming scheme 1987export octave_name=legendre_sphPlm 1988export funcname=gsl_sf_legendre_sphPlm_e 1989${RT} IID_D >> gsl_sf.cc 1990 1991 1992# (int, int, double, double) to double ############################### 1993 1994export octave_name=gsl_sf_hydrogenicR 1995export funcname=gsl_sf_hydrogenicR_e 1996cat << \EOF > docstring.txt 1997This routine computes the n-th normalized hydrogenic bound state 1998radial wavefunction, 1999@tex 2000R_n := 2 (Z^{3/2}/n^2) \sqrt{(n-l-1)!/(n+l)!} \exp(-Z r/n) 2001 (2Zr/n)^l L^{2l+1}_{n-l-1}(2Zr/n). 2002@end tex 2003@ifnottex 2004 2005@example 2006@group 2007 Z^(3/2) ---------------- -Z r/n l 2l+1 2008R_n := 2 -------- \ / (n-l-1)!/(n+l)! . e . (2Zr/n) . L (2Zr/n). 2009 n^2 v n-l-1 2010@end group 2011@end example 2012 2013@end ifnottex 2014where @math{L^a_b(x)} is the generalized Laguerre polynomial. 2015The normalization is chosen such that the wavefunction \psi 2016is given by @math{\psi(n,l,r) = R_n Y_{lm}}. 2017EOF 2018${RT} IIDD_D >> gsl_sf.cc 2019 2020###################################################################### 2021 2022export octave_name=gsl_sf_mathieu_Mc 2023export funcname=gsl_sf_mathieu_Mc_e 2024cat << \EOF > docstring.txt 2025This routine computes the radial j-th kind Mathieu function 2026@math{Mc_n^{(j)}(q,x)} of order n. 2027EOF 2028${RT} IIDD_D >> gsl_sf.cc 2029 2030###################################################################### 2031 2032export octave_name=gsl_sf_mathieu_Ms 2033export funcname=gsl_sf_mathieu_Ms_e 2034cat << \EOF > docstring.txt 2035This routine computes the radial j-th kind Mathieu function 2036@math{Ms_n^{(j)}(q,x)} of order n. 2037EOF 2038${RT} IIDD_D >> gsl_sf.cc 2039 2040 2041# (double, int) to double ############################################ 2042 2043export octave_name=gsl_sf_bessel_zero_Jnu 2044export funcname=gsl_sf_bessel_zero_Jnu_e 2045cat << \EOF > docstring.txt 2046Computes the location of the n-th positive zero of the 2047Bessel function J_x(). 2048EOF 2049${RT} DI_D >> gsl_sf.cc 2050 2051 2052# (double, double, double) to double ################################# 2053 2054export octave_name=gsl_sf_hyperg_U 2055export funcname=gsl_sf_hyperg_U_e 2056cat << \EOF > docstring.txt 2057Secondary Confluent Hypergoemetric U function A&E 13.1.3 2058All inputs are double as is the output. 2059EOF 2060${RT} DDD_D >> gsl_sf.cc 2061 2062## Deprecated naming scheme 2063export octave_name=hyperg_U 2064export funcname=gsl_sf_hyperg_U_e 2065${RT} DDD_D >> gsl_sf.cc 2066 2067###################################################################### 2068 2069export octave_name=gsl_sf_hyperg_1F1 2070export funcname=gsl_sf_hyperg_1F1_e 2071cat << \EOF > docstring.txt 2072Primary Confluent Hypergoemetric U function A&E 13.1.3 2073All inputs are double as is the output. 2074EOF 2075${RT} DDD_D >> gsl_sf.cc 2076 2077## Deprecated naming scheme 2078export octave_name=hyperg_1F1 2079export funcname=gsl_sf_hyperg_1F1_e 2080${RT} DDD_D >> gsl_sf.cc 2081 2082###################################################################### 2083 2084export octave_name=gsl_sf_hyperg_2F0 2085export funcname=gsl_sf_hyperg_2F0_e 2086cat << \EOF > docstring.txt 2087Computes the hypergeometric function 2F0(a,b,x). 2088The series representation is a divergent hypergeometric series. 2089However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,-1/x) 2090EOF 2091${RT} DDD_D >> gsl_sf.cc 2092 2093## Deprecated naming scheme 2094export octave_name=hyperg_2F0 2095export funcname=gsl_sf_hyperg_2F0_e 2096${RT} DDD_D >> gsl_sf.cc 2097 2098###################################################################### 2099 2100export octave_name=gsl_sf_beta_inc 2101export funcname=gsl_sf_beta_inc_e 2102cat << \EOF > docstring.txt 2103Computes the normalized incomplete Beta function 2104 2105 I_x(a,b)=B_x(a,b)/B(a,b) 2106 2107where @math{B_x(a,b) = \int_0^x t^(a-1) (1-t)^(b-1) dt} 2108for @math{0 \le x \le 1}. 2109 2110For a > 0, b > 0 the value is computed using a continued fraction 2111expansion. For all other values it is computed using the relation 2112 I_x(a,b,x) = (1/a) x^a 2F1(a,1-b,a+1,x)/B(a,b). 2113EOF 2114${RT} DDD_D >> gsl_sf.cc 2115 2116 2117# (double, double, double, double) to double ######################### 2118 2119export octave_name=gsl_sf_hyperg_2F1 2120export funcname=gsl_sf_hyperg_2F1_e 2121cat << \EOF > docstring.txt 2122Computes the Gauss hypergeometric function 21232F1(a,b,c,x) = F(a,b,c,x) for |x| < 1. 2124If the arguments (a,b,c,x) are too close to a singularity then 2125the function can return the error code GSL_EMAXITER when the 2126series approximation converges too slowly. 2127This occurs in the region of x=1, c - a - b = m for integer m. 2128EOF 2129${RT} DDDD_D >> gsl_sf.cc 2130 2131 2132# unsigned int to double ############################################# 2133 2134export octave_name=gsl_sf_fact 2135export funcname=gsl_sf_fact_e 2136cat << \EOF > docstring.txt 2137Computes the factorial n!. The factorial is related to the Gamma 2138function by n! = \Gamma(n+1). The maximum value of n such that n! is 2139not considered an overflow is 170. 2140EOF 2141${RT} U_D >> gsl_sf.cc 2142 2143###################################################################### 2144 2145export octave_name=gsl_sf_doublefact 2146export funcname=gsl_sf_doublefact_e 2147cat << \EOF > docstring.txt 2148Compute the double factorial n!! = n(n-2)(n-4)\dots. The maximum value 2149of n such that n!! is not considered an overflow is 297. 2150EOF 2151${RT} U_D >> gsl_sf.cc 2152 2153###################################################################### 2154 2155export octave_name=gsl_sf_lnfact 2156export funcname=gsl_sf_lnfact_e 2157cat << \EOF > docstring.txt 2158Computes the logarithm of the factorial of n, 2159\log(n!). The algorithm is faster than computing \ln(\Gamma(n+1)) via 2160gsl_sf_lngamma for n < 170, but defers for larger n. 2161EOF 2162${RT} U_D >> gsl_sf.cc 2163 2164###################################################################### 2165 2166export octave_name=gsl_sf_lndoublefact 2167export funcname=gsl_sf_lndoublefact_e 2168cat << \EOF > docstring.txt 2169Computes the logarithm of the double factorial of n, \log(n!!). 2170EOF 2171${RT} U_D >> gsl_sf.cc 2172 2173 2174# (unsigned int, unsigned int) to double ############################# 2175 2176export octave_name=gsl_sf_choose 2177export funcname=gsl_sf_choose_e 2178cat << \EOF > docstring.txt 2179Computes the combinatorial factor n choose m = n!/(m!(n-m)!). 2180EOF 2181${RT} UU_D >> gsl_sf.cc 2182 2183###################################################################### 2184 2185export octave_name=gsl_sf_lnchoose 2186export funcname=gsl_sf_lnchoose_e 2187cat << \EOF > docstring.txt 2188Computes the logarithm of n choose m. This is equivalent to 2189\log(n!) - \log(m!) - \log((n-m)!). 2190EOF 2191${RT} UU_D >> gsl_sf.cc 2192 2193 2194# (int, int, int, int, int, int) to double ########################### 2195 2196export octave_name=gsl_sf_coupling_3j 2197export funcname=gsl_sf_coupling_3j_e 2198cat << \EOF > docstring.txt 2199computes the Wigner 3-j coefficient, 2200 2201@example 2202@group 2203(ja jb jc 2204 ma mb mc) 2205@end group 2206@end example 2207 2208where the arguments are given in half-integer units, 2209@code{ja = two_ja/2}, @code{ma = two_ma/2}, etc. 2210EOF 2211${RT} IIIIII_D >> gsl_sf.cc 2212 2213## Deprecated naming scheme 2214export octave_name=coupling_3j 2215export funcname=gsl_sf_coupling_3j_e 2216${RT} IIIIII_D >> gsl_sf.cc 2217 2218###################################################################### 2219 2220export octave_name=gsl_sf_coupling_6j 2221export funcname=gsl_sf_coupling_6j_e 2222cat << \EOF > docstring.txt 2223computes the Wigner 6-j coefficient, 2224 2225@example 2226@group 2227@{ja jb jc 2228 jd je jf@} 2229@end group 2230@end example 2231 2232where the arguments are given in half-integer units, 2233@code{ja = two_ja/2}, @code{jd = two_jd/2}, etc. 2234EOF 2235${RT} IIIIII_D >> gsl_sf.cc 2236 2237## Deprecated naming scheme 2238export octave_name=coupling_6j 2239export funcname=gsl_sf_coupling_6j_e 2240${RT} IIIIII_D >> gsl_sf.cc 2241 2242 2243# (int, int, int, int, int, int, int, int, int) to double ############ 2244 2245export octave_name=gsl_sf_coupling_9j 2246export funcname=gsl_sf_coupling_9j_e 2247cat << \EOF > docstring.txt 2248computes the Wigner 9-j coefficient, 2249 2250@example 2251@group 2252@{ja jb jc 2253 jd je jf 2254 jg jh ji@} 2255@end group 2256@end example 2257 2258where the arguments are given in half-integer units, 2259@code{ja = two_ja/2}, @code{jd = two_jd/2}, etc. 2260EOF 2261${RT} IIIIIIIII_D >> gsl_sf.cc 2262 2263## Deprecated naming scheme 2264export octave_name=coupling_9j 2265export funcname=gsl_sf_coupling_9j_e 2266${RT} IIIIIIIII_D >> gsl_sf.cc 2267 2268 2269############################# 2270## gsl_sf_*_array function ## 2271############################# 2272 2273# (length, double) ################################################### 2274 2275export octave_name=gsl_sf_bessel_jl_array 2276export funcname=gsl_sf_bessel_jl_array 2277cat << \EOF > docstring.txt 2278Computes the values of the regular spherical Bessel functions j_l(x) 2279for l from 0 to lmax inclusive for lmax >= 0 and x >= 0. The values 2280are computed using recurrence relations for efficiency, and therefore 2281may differ slightly from the exact values. 2282EOF 2283${RT} LD_D_array >> gsl_sf.cc 2284 2285###################################################################### 2286 2287export octave_name=gsl_sf_bessel_jl_steed_array 2288export funcname=gsl_sf_bessel_jl_steed_array 2289cat << \EOF > docstring.txt 2290This routine uses Steed’s method to compute the values of the regular 2291spherical Bessel functions j_l(x) for l from 0 to lmax inclusive for 2292lmax >= 0 and x >= 0. The Steed/Barnett algorithm is described in 2293Comp. Phys. Comm. 21, 297 (1981). Steed’s method is more stable than 2294the recurrence used in the other functions but is also slower. 2295EOF 2296${RT} LD_D_array >> gsl_sf.cc 2297 2298###################################################################### 2299 2300export octave_name=gsl_sf_bessel_il_scaled_array 2301export funcname=gsl_sf_bessel_il_scaled_array 2302cat << \EOF > docstring.txt 2303This routine computes the values of the scaled regular modified 2304spherical Bessel functions \exp(-|x|) i_l(x) for l from 0 to lmax 2305inclusive for lmax >= 0. The values are computed using recurrence 2306relations for efficiency, and therefore may differ slightly from the 2307exact values. 2308EOF 2309${RT} LD_D_array >> gsl_sf.cc 2310 2311###################################################################### 2312 2313export octave_name=gsl_sf_bessel_kl_scaled_array 2314export funcname=gsl_sf_bessel_kl_scaled_array 2315cat << \EOF > docstring.txt 2316This routine computes the values of the scaled irregular modified 2317spherical Bessel functions \exp(x) k_l(x) for l from 0 to lmax 2318inclusive for lmax >= 0 and x>0. The values are computed using 2319recurrence relations for efficiency, and therefore may differ slightly 2320from the exact values. 2321EOF 2322${RT} LD_D_array >> gsl_sf.cc 2323 2324###################################################################### 2325 2326export octave_name=gsl_sf_bessel_yl_array 2327export funcname=gsl_sf_bessel_yl_array 2328cat << \EOF > docstring.txt 2329This routine computes the values of the irregular spherical Bessel 2330functions y_l(x) for l from 0 to lmax inclusive for lmax >= 0. The 2331values are computed using recurrence relations for efficiency, and 2332therefore may differ slightly from the exact values. 2333EOF 2334${RT} LD_D_array >> gsl_sf.cc 2335 2336###################################################################### 2337 2338export octave_name=gsl_sf_legendre_Pl_array 2339export funcname=gsl_sf_legendre_Pl_array 2340cat << \EOF > docstring.txt 2341These functions compute arrays of Legendre polynomials P_l(x) and 2342derivatives dP_l(x)/dx, for l = 0, \dots, lmax, |x| <= 1. 2343EOF 2344${RT} LD_D_array >> gsl_sf.cc 2345 2346 2347# (length, double, double) ########################################### 2348 2349export octave_name=gsl_sf_gegenpoly_array 2350export funcname=gsl_sf_gegenpoly_array 2351cat << \EOF > docstring.txt 2352This function computes an array of Gegenbauer polynomials 2353@math{C^{(\lambda)}_n(x)} for n = 0, 1, 2, \dots, nmax, subject to 2354@math{\lambda > -1/2}, @math{nmax} @geq{} @math{0}. 2355EOF 2356${RT} LDD_D_array >> gsl_sf.cc 2357 2358 2359# (min, max, double) ################################################# 2360 2361export octave_name=gsl_sf_bessel_In_array 2362export funcname=gsl_sf_bessel_In_array 2363cat << \EOF > docstring.txt 2364his routine computes the values of the regular modified cylindrical 2365Bessel functions I_n(x) for n from nmin to nmax inclusive. The start 2366of the range nmin must be positive or zero. The values are computed 2367using recurrence relations for efficiency, and therefore may differ 2368slightly from the exact values. 2369EOF 2370${RT} LLD_D_array >> gsl_sf.cc 2371 2372###################################################################### 2373 2374export octave_name=gsl_sf_bessel_In_scaled_array 2375export funcname=gsl_sf_bessel_In_scaled_array 2376cat << \EOF > docstring.txt 2377This routine computes the values of the scaled regular cylindrical 2378Bessel functions \exp(-|x|) I_n(x) for n from nmin to nmax 2379inclusive. The start of the range nmin must be positive or zero. The 2380values are computed using recurrence relations for efficiency, and 2381therefore may differ slightly from the exact values. 2382EOF 2383${RT} LLD_D_array >> gsl_sf.cc 2384 2385###################################################################### 2386 2387export octave_name=gsl_sf_bessel_Jn_array 2388export funcname=gsl_sf_bessel_Jn_array 2389cat << \EOF > docstring.txt 2390This routine computes the values of the regular cylindrical Bessel 2391functions J_n(x) for n from nmin to nmax inclusive. The values are 2392computed using recurrence relations for efficiency, and therefore may 2393differ slightly from the exact values. 2394EOF 2395${RT} LLD_D_array >> gsl_sf.cc 2396 2397###################################################################### 2398 2399export octave_name=gsl_sf_bessel_Kn_array 2400export funcname=gsl_sf_bessel_Kn_array 2401cat << \EOF > docstring.txt 2402This routine computes the values of the irregular modified cylindrical 2403Bessel functions K_n(x) for n from nmin to nmax inclusive. The start 2404of the range nmin must be positive or zero. The domain of the function 2405is x>0. The values are computed using recurrence relations for 2406efficiency, and therefore may differ slightly from the exact values. 2407EOF 2408${RT} LLD_D_array >> gsl_sf.cc 2409 2410###################################################################### 2411 2412export octave_name=gsl_sf_bessel_Kn_scaled_array 2413export funcname=gsl_sf_bessel_Kn_scaled_array 2414cat << \EOF > docstring.txt 2415This routine computes the values of the scaled irregular cylindrical 2416Bessel functions \exp(x) K_n(x) for n from nmin to nmax inclusive. The 2417start of the range nmin must be positive or zero. The domain of the 2418function is x>0. The values are computed using recurrence relations 2419for efficiency, and therefore may differ slightly from the exact 2420values. 2421EOF 2422${RT} LLD_D_array >> gsl_sf.cc 2423 2424###################################################################### 2425 2426export octave_name=gsl_sf_bessel_Yn_array 2427export funcname=gsl_sf_bessel_Yn_array 2428cat << \EOF > docstring.txt 2429This routine computes the values of the irregular cylindrical Bessel 2430functions Y_n(x) for n from nmin to nmax inclusive. The domain of the 2431function is x>0. The values are computed using recurrence relations 2432for efficiency, and therefore may differ slightly from the exact 2433values. 2434EOF 2435${RT} LLD_D_array >> gsl_sf.cc 2436 2437 2438# (length, int, double) to double #################################### 2439 2440# DEPRECATED: gsl_sf_legendre_Plm_array 2.0 2441export octave_name=gsl_sf_legendre_Plm_array 2442export funcname=gsl_sf_legendre_Plm_array 2443cat << \EOF > docstring.txt 2444Compute arrays of Legendre polynomials P_l^m(x) for m >= 0, l = |m|, 2445..., lmax, |x| <= 1. 2446EOF 2447${RT} LID_D_array >> gsl_sf.cc 2448 2449###################################################################### 2450 2451# DEPRECATED: gsl_sf_legendre_Plm_deriv_array 2.0 2452export octave_name=gsl_sf_legendre_Plm_deriv_array 2453export funcname=gsl_sf_legendre_Plm_deriv_array 2454cat << \EOF > docstring.txt 2455Compute arrays of Legendre polynomials P_l^m(x) and derivatives 2456dP_l^m(x)/dx for m >= 0, l = |m|, ..., lmax, |x| <= 1. 2457EOF 2458${RT} LID_DD_array >> gsl_sf.cc 2459 2460###################################################################### 2461 2462# DEPRECATED: gsl_sf_legendre_sphPlm_array 2.0 2463export octave_name=gsl_sf_legendre_sphPlm_array 2464export funcname=gsl_sf_legendre_sphPlm_array 2465cat << \EOF > docstring.txt 2466Computes an array of normalized associated Legendre functions 2467@iftex 2468@tex 2469$\\sqrt{(2l+1)/(4\\pi)} \\sqrt{(l-m)!/(l+m)!} P_l^m(x)$ 2470for $m >= 0, l = |m|, ..., lmax, |x| <= 1.0$ 2471@end tex 2472@end iftex 2473@ifinfo 2474sqrt((2l+1)/(4*pi)) * sqrt((l-m)!/(l+m)!) Plm (x) 2475for m >= 0, l = |m|, ..., lmax, |x| <= 1.0 2476@end ifinfo 2477EOF 2478${RT} LID_D_array >> gsl_sf.cc 2479 2480## Deprecated naming scheme 2481export octave_name=legendre_sphPlm_array 2482export funcname=gsl_sf_legendre_sphPlm_array 2483${RT} LID_D_array >> gsl_sf.cc 2484 2485###################################################################### 2486 2487# DEPRECATED: gsl_sf_legendre_sphPlm_deriv_array 2.0 2488export octave_name=gsl_sf_legendre_sphPlm_deriv_array 2489export funcname=gsl_sf_legendre_sphPlm_deriv_array 2490cat << \EOF > docstring.txt 2491Computes an array of normalized associated Legendre functions 2492@iftex 2493@tex 2494$\\sqrt{(2l+1)/(4\\pi)} \\sqrt{(l-m)!/(l+m)!} P_l^m(x)$ 2495for $m \geq 0, l = |m|, ..., lmax, |x| <= 1.0$ 2496@end tex 2497@end iftex 2498@ifinfo 2499sqrt((2l+1)/(4*pi)) * sqrt((l-m)!/(l+m)!) Plm (x) 2500for m >= 0, l = |m|, ..., lmax, |x| <= 1.0 2501@end ifinfo 2502and their derivatives. 2503EOF 2504${RT} LID_DD_array >> gsl_sf.cc 2505 2506###################################################################### 2507 2508export octave_name=gsl_sf_legendre_array 2509export funcname=gsl_sf_legendre_array_e 2510cat << \EOF > docstring.txt 2511Calculate all normalized associated Legendre polynomials for 0 <= l <= 2512lmax and 0 <= m <= l for |x| <= 1. The norm parameter specifies which 2513normalization is used. The array index of P_l^m is given by 2514l(l+1)/2+m. To include or exclude the Condon-Shortley phase factor of 2515(-1)^m, set the fourth parameter to either -1 or 1, respectively. 2516 2517EOF 2518${RT} NSDD_D_array >> gsl_sf.cc 2519 2520###################################################################### 2521 2522export octave_name=gsl_sf_legendre_deriv_array 2523export funcname=gsl_sf_legendre_deriv_array_e 2524cat << \EOF > docstring.txt 2525Calculate all normalized associated Legendre polynomials and their 2526first derivatives for 0 <= l <= lmax and 0 <= m <= l for |x| <= 1. The 2527norm parameter specifies which normalization is used. The array index 2528of P_l^m is given by l(l+1)/2+m. To include or exclude the 2529Condon-Shortley phase factor of (-1)^m, set the fourth parameter to 2530either -1 or 1, respectively. 2531EOF 2532${RT} NSDD_DD_array >> gsl_sf.cc 2533 2534###################################################################### 2535 2536export octave_name=legendre_deriv2_array 2537export funcname=gsl_sf_legendre_deriv2_array_e 2538cat << \EOF > docstring.txt 2539Calculate all normalized associated Legendre polynomials and their 2540first and second derivatives for 0 <= l <= lmax and 0 <= m <= l for |x| <= 1. The 2541norm parameter specifies which normalization is used. The array index 2542of P_l^m is given by l(l+1)/2+m. To include or exclude the 2543Condon-Shortley phase factor of (-1)^m, set the fourth parameter to 2544either -1 or 1, respectively. 2545EOF 2546${RT} NSDD_DDD_array >> gsl_sf.cc 2547 2548 2549###################################################################### 2550## Zeta and related functions ## 2551###################################################################### 2552 2553 2554## Riemann zeta function 2555 2556export octave_name=gsl_sf_zeta 2557export funcname=gsl_sf_zeta_e 2558cat << \EOF > docstring.txt 2559Computes the Riemann zeta function \zeta(s) for 2560arbitrary s, s \ne 1. 2561 2562The Riemann zeta function is defined by the infinite sum 2563\zeta(s) = \sum_@{k=1@}^\infty k^@{-s@}. 2564EOF 2565${RT} D_D >> gsl_sf.cc 2566 2567## Deprecated naming scheme (package release 2.0.0) 2568export octave_name=gsl_zt_zeta 2569export funcname=gsl_sf_zeta_e 2570${RT} D_D >> gsl_sf.cc 2571 2572## Deprecated naming scheme (package release < 2.0.0) 2573export octave_name=zeta 2574export funcname=gsl_sf_zeta_e 2575${RT} D_D >> gsl_sf.cc 2576 2577export octave_name=gsl_sf_zeta_int 2578export funcname=gsl_sf_zeta_int_e 2579cat << \EOF > docstring.txt 2580Computes the Riemann zeta function \zeta(n) for 2581integer n, n \ne 1. 2582EOF 2583${RT} I_D >> gsl_sf.cc 2584 2585## Deprecated naming scheme (package release < 2.0.0) 2586export octave_name=zeta_int 2587export funcname=gsl_sf_zeta_int_e 2588${RT} I_D >> gsl_sf.cc 2589 2590 2591## Riemann zeta function minus one 2592 2593export octave_name=gsl_sf_zetam1 2594export funcname=gsl_sf_zetam1_e 2595cat << \EOF > docstring.txt 2596Computes \zeta(s) - 1 for arbitrary s, s \ne 1, where \zeta 2597denotes the Riemann zeta function. 2598 2599@seealso{gsl_sf_zeta} 2600EOF 2601${RT} D_D >> gsl_sf.cc 2602 2603export octave_name=gsl_sf_zetam1_int 2604export funcname=gsl_sf_zetam1_int_e 2605cat << \EOF > docstring.txt 2606Computes \zeta(s) - 1 for integer n, n \ne 1, where \zeta 2607denotes the Riemann zeta function. 2608 2609@seealso{gsl_sf_zetam1, gsl_sf_zeta, gsl_sf_zeta_int} 2610EOF 2611${RT} I_D >> gsl_sf.cc 2612 2613 2614## Dirichlet eta function 2615 2616export octave_name=gsl_sf_eta 2617export funcname=gsl_sf_eta_e 2618cat << \EOF > docstring.txt 2619Computes the eta function \eta(s) for arbitrary s. 2620 2621The eta function is defined by \eta(s) = (1-2^@{1-s@}) \zeta 2622EOF 2623${RT} D_D >> gsl_sf.cc 2624 2625## Deprecated naming scheme 2626export octave_name=eta 2627export funcname=gsl_sf_eta_e 2628${RT} D_D >> gsl_sf.cc 2629 2630export octave_name=gsl_sf_eta_int 2631export funcname=gsl_sf_eta_int_e 2632cat << \EOF > docstring.txt 2633Computes the eta function \eta(n) for integer n. 2634EOF 2635${RT} I_D >> gsl_sf.cc 2636 2637## Deprecated naming scheme 2638export octave_name=eta_int 2639export funcname=gsl_sf_eta_int_e 2640${RT} I_D >> gsl_sf.cc 2641 2642 2643## Hurwitz zeta function 2644 2645export octave_name=gsl_sf_hzeta 2646export funcname=gsl_sf_hzeta_e 2647cat << \EOF > docstring.txt 2648Computes the Hurwitz zeta function \zeta(s,q) 2649for s > 1, q > 0. 2650EOF 2651${RT} DD_D >> gsl_sf.cc 2652 2653## Deprecated naming scheme 2654export octave_name=hzeta 2655export funcname=gsl_sf_hzeta_e 2656${RT} DD_D >> gsl_sf.cc 2657