Small formatting tweak in SF docs.
[Math-GSL.git] / SF.i
blob5382020527e6a2359bd10350d406e015c1563f97
1 %module "Math::GSL::SF"
2 %include "typemaps.i"
3 %{
4 #include "gsl/gsl_mode.h"
5 #include "gsl/gsl_sf.h"
6 #include "gsl/gsl_sf_airy.h"
7 #include "gsl/gsl_sf_bessel.h"
8 #include "gsl/gsl_sf_clausen.h"
9 #include "gsl/gsl_sf_coulomb.h"
10 #include "gsl/gsl_sf_coupling.h"
11 #include "gsl/gsl_sf_dawson.h"
12 #include "gsl/gsl_sf_debye.h"
13 #include "gsl/gsl_sf_dilog.h"
14 #include "gsl/gsl_sf_elementary.h"
15 #include "gsl/gsl_sf_ellint.h"
16 #include "gsl/gsl_sf_elljac.h"
17 #include "gsl/gsl_sf_erf.h"
18 #include "gsl/gsl_sf_exp.h"
19 #include "gsl/gsl_sf_expint.h"
20 #include "gsl/gsl_sf_fermi_dirac.h"
21 #include "gsl/gsl_sf_gamma.h"
22 #include "gsl/gsl_sf_gegenbauer.h"
23 #include "gsl/gsl_sf_hyperg.h"
24 #include "gsl/gsl_sf_laguerre.h"
25 #include "gsl/gsl_sf_lambert.h"
26 #include "gsl/gsl_sf_legendre.h"
27 #include "gsl/gsl_sf_log.h"
28 #include "gsl/gsl_sf_mathieu.h"
29 #include "gsl/gsl_sf_pow_int.h"
30 #include "gsl/gsl_sf_psi.h"
31 #include "gsl/gsl_sf_result.h"
32 #include "gsl/gsl_sf_synchrotron.h"
33 #include "gsl/gsl_sf_transport.h"
34 #include "gsl/gsl_sf_trig.h"
35 #include "gsl/gsl_sf_zeta.h"
38 %include "gsl/gsl_mode.h"
39 %include "gsl/gsl_sf.h"
40 %include "gsl/gsl_sf_airy.h"
41 %include "gsl/gsl_sf_bessel.h"
42 %include "gsl/gsl_sf_clausen.h"
43 %include "gsl/gsl_sf_coulomb.h"
44 %include "gsl/gsl_sf_coupling.h"
45 %include "gsl/gsl_sf_dawson.h"
46 %include "gsl/gsl_sf_debye.h"
47 %include "gsl/gsl_sf_dilog.h"
48 %include "gsl/gsl_sf_elementary.h"
49 %include "gsl/gsl_sf_ellint.h"
50 %include "gsl/gsl_sf_elljac.h"
51 %include "gsl/gsl_sf_erf.h"
52 %include "gsl/gsl_sf_exp.h"
53 %include "gsl/gsl_sf_expint.h"
54 %include "gsl/gsl_sf_fermi_dirac.h"
55 %include "gsl/gsl_sf_gamma.h"
56 %include "gsl/gsl_sf_gegenbauer.h"
57 %include "gsl/gsl_sf_hyperg.h"
58 %include "gsl/gsl_sf_laguerre.h"
59 %include "gsl/gsl_sf_lambert.h"
60 %include "gsl/gsl_sf_legendre.h"
61 %include "gsl/gsl_sf_log.h"
62 %include "gsl/gsl_sf_mathieu.h"
63 %include "gsl/gsl_sf_pow_int.h"
64 %include "gsl/gsl_sf_psi.h"
65 %include "gsl/gsl_sf_result.h"
66 %include "gsl/gsl_sf_synchrotron.h"
67 %include "gsl/gsl_sf_transport.h"
68 %include "gsl/gsl_sf_trig.h"
69 %include "gsl/gsl_sf_zeta.h"
72 %perlcode %{
74 @EXPORT_airy = qw/
75 gsl_sf_airy_Ai_e
76 gsl_sf_airy_Ai
77 gsl_sf_airy_Bi_e
78 gsl_sf_airy_Bi
79 gsl_sf_airy_Ai_scaled_e
80 gsl_sf_airy_Ai_scaled
81 gsl_sf_airy_Bi_scaled_e
82 gsl_sf_airy_Bi_scaled
83 gsl_sf_airy_Ai_deriv_e
84 gsl_sf_airy_Ai_deriv
85 gsl_sf_airy_Bi_deriv_e
86 gsl_sf_airy_Bi_deriv
87 gsl_sf_airy_Ai_deriv_scaled_e
88 gsl_sf_airy_Ai_deriv_scaled
89 gsl_sf_airy_Bi_deriv_scaled_e
90 gsl_sf_airy_Bi_deriv_scaled
91 gsl_sf_airy_zero_Ai_e
92 gsl_sf_airy_zero_Ai
93 gsl_sf_airy_zero_Bi_e
94 gsl_sf_airy_zero_Bi
95 gsl_sf_airy_zero_Ai_deriv_e
96 gsl_sf_airy_zero_Ai_deriv
97 gsl_sf_airy_zero_Bi_deriv_e
98 gsl_sf_airy_zero_Bi_deriv
100 @EXPORT_bessel =qw/
101 gsl_sf_bessel_J0_e
102 gsl_sf_bessel_J0
103 gsl_sf_bessel_J1_e
104 gsl_sf_bessel_J1
105 gsl_sf_bessel_Jn_e
106 gsl_sf_bessel_Jn
107 gsl_sf_bessel_Jn_array
108 gsl_sf_bessel_Y0_e
109 gsl_sf_bessel_Y0
110 gsl_sf_bessel_Y1_e
111 gsl_sf_bessel_Y1
112 gsl_sf_bessel_Yn_e
113 gsl_sf_bessel_Yn
114 gsl_sf_bessel_Yn_array
115 gsl_sf_bessel_I0_e
116 gsl_sf_bessel_I0
117 gsl_sf_bessel_I1_e
118 gsl_sf_bessel_I1
119 gsl_sf_bessel_In_e
120 gsl_sf_bessel_In
121 gsl_sf_bessel_In_array
122 gsl_sf_bessel_I0_scaled_e
123 gsl_sf_bessel_I0_scaled
124 gsl_sf_bessel_I1_scaled_e
125 gsl_sf_bessel_I1_scaled
126 gsl_sf_bessel_In_scaled_e
127 gsl_sf_bessel_In_scaled
128 gsl_sf_bessel_In_scaled_array
129 gsl_sf_bessel_K0_e
130 gsl_sf_bessel_K0
131 gsl_sf_bessel_K1_e
132 gsl_sf_bessel_K1
133 gsl_sf_bessel_Kn_e
134 gsl_sf_bessel_Kn
135 gsl_sf_bessel_Kn_array
136 gsl_sf_bessel_K0_scaled_e
137 gsl_sf_bessel_K0_scaled
138 gsl_sf_bessel_K1_scaled_e
139 gsl_sf_bessel_K1_scaled
140 gsl_sf_bessel_Kn_scaled_e
141 gsl_sf_bessel_Kn_scaled
142 gsl_sf_bessel_Kn_scaled_array
143 gsl_sf_bessel_j0_e
144 gsl_sf_bessel_j0
145 gsl_sf_bessel_j1_e
146 gsl_sf_bessel_j1
147 gsl_sf_bessel_j2_e
148 gsl_sf_bessel_j2
149 gsl_sf_bessel_jl_e
150 gsl_sf_bessel_jl
151 gsl_sf_bessel_jl_array
152 gsl_sf_bessel_jl_steed_array
153 gsl_sf_bessel_y0_e
154 gsl_sf_bessel_y0
155 gsl_sf_bessel_y1_e
156 gsl_sf_bessel_y1
157 gsl_sf_bessel_y2_e
158 gsl_sf_bessel_y2
159 gsl_sf_bessel_yl_e
160 gsl_sf_bessel_yl
161 gsl_sf_bessel_yl_array
162 gsl_sf_bessel_i0_scaled_e
163 gsl_sf_bessel_i0_scaled
164 gsl_sf_bessel_i1_scaled_e
165 gsl_sf_bessel_i1_scaled
166 gsl_sf_bessel_i2_scaled_e
167 gsl_sf_bessel_i2_scaled
168 gsl_sf_bessel_il_scaled_e
169 gsl_sf_bessel_il_scaled
170 gsl_sf_bessel_il_scaled_array
171 gsl_sf_bessel_k0_scaled_e
172 gsl_sf_bessel_k0_scaled
173 gsl_sf_bessel_k1_scaled_e
174 gsl_sf_bessel_k1_scaled
175 gsl_sf_bessel_k2_scaled_e
176 gsl_sf_bessel_k2_scaled
177 gsl_sf_bessel_kl_scaled_e
178 gsl_sf_bessel_kl_scaled
179 gsl_sf_bessel_kl_scaled_array
180 gsl_sf_bessel_Jnu_e
181 gsl_sf_bessel_Jnu
182 gsl_sf_bessel_Ynu_e
183 gsl_sf_bessel_Ynu
184 gsl_sf_bessel_sequence_Jnu_e
185 gsl_sf_bessel_Inu_scaled_e
186 gsl_sf_bessel_Inu_scaled
187 gsl_sf_bessel_Inu_e
188 gsl_sf_bessel_Inu
189 gsl_sf_bessel_Knu_scaled_e
190 gsl_sf_bessel_Knu_scaled
191 gsl_sf_bessel_Knu_e
192 gsl_sf_bessel_Knu
193 gsl_sf_bessel_lnKnu_e
194 gsl_sf_bessel_lnKnu
195 gsl_sf_bessel_zero_J0_e
196 gsl_sf_bessel_zero_J0
197 gsl_sf_bessel_zero_J1_e
198 gsl_sf_bessel_zero_J1
199 gsl_sf_bessel_zero_Jnu_e
200 gsl_sf_bessel_zero_Jnu
202 @EXPORT_clausen = qw/
203 gsl_sf_clausen_e
204 gsl_sf_clausen
206 @EXPORT_hydrogenic = qw/
207 gsl_sf_hydrogenicR_1_e
208 gsl_sf_hydrogenicR_1
209 gsl_sf_hydrogenicR_e
210 gsl_sf_hydrogenicR
212 @EXPORT_coulumb = qw/
213 gsl_sf_coulomb_wave_FG_e
214 gsl_sf_coulomb_wave_F_array
215 gsl_sf_coulomb_wave_FG_array
216 gsl_sf_coulomb_wave_FGp_array
217 gsl_sf_coulomb_wave_sphF_array
218 gsl_sf_coulomb_CL_e
219 gsl_sf_coulomb_CL_array
221 @EXPORT_coupling = qw/
222 gsl_sf_coupling_3j_e
223 gsl_sf_coupling_3j
224 gsl_sf_coupling_6j_e
225 gsl_sf_coupling_6j
226 gsl_sf_coupling_RacahW_e
227 gsl_sf_coupling_RacahW
228 gsl_sf_coupling_9j_e
229 gsl_sf_coupling_9j
230 gsl_sf_coupling_6j_INCORRECT_e
231 gsl_sf_coupling_6j_INCORRECT
233 @EXPORT_dawson = qw/
234 gsl_sf_dawson_e
235 gsl_sf_dawson
237 @EXPORT_debye = qw/
238 gsl_sf_debye_1_e
239 gsl_sf_debye_1
240 gsl_sf_debye_2_e
241 gsl_sf_debye_2
242 gsl_sf_debye_3_e
243 gsl_sf_debye_3
244 gsl_sf_debye_4_e
245 gsl_sf_debye_4
246 gsl_sf_debye_5_e
247 gsl_sf_debye_5
248 gsl_sf_debye_6_e
249 gsl_sf_debye_6
251 @EXPORT_dilog = qw/
252 gsl_sf_dilog_e
253 gsl_sf_dilog
254 gsl_sf_complex_dilog_xy_e
255 gsl_sf_complex_dilog_e
258 @EXPORT_misc = qw/
259 gsl_sf_complex_spence_xy_e
260 gsl_sf_multiply_e
261 gsl_sf_multiply
262 gsl_sf_multiply_err_e
264 @EXPORT_elliptic = qw/
265 gsl_sf_ellint_Kcomp_e
266 gsl_sf_ellint_Kcomp
267 gsl_sf_ellint_Ecomp_e
268 gsl_sf_ellint_Ecomp
269 gsl_sf_ellint_Pcomp_e
270 gsl_sf_ellint_Pcomp
271 gsl_sf_ellint_Dcomp_e
272 gsl_sf_ellint_Dcomp
273 gsl_sf_ellint_F_e
274 gsl_sf_ellint_F
275 gsl_sf_ellint_E_e
276 gsl_sf_ellint_E
277 gsl_sf_ellint_P_e
278 gsl_sf_ellint_P
279 gsl_sf_ellint_D_e
280 gsl_sf_ellint_D
281 gsl_sf_ellint_RC_e
282 gsl_sf_ellint_RC
283 gsl_sf_ellint_RD_e
284 gsl_sf_ellint_RD
285 gsl_sf_ellint_RF_e
286 gsl_sf_ellint_RF
287 gsl_sf_ellint_RJ_e
288 gsl_sf_ellint_RJ
289 gsl_sf_elljac_e
291 @EXPORT_error = qw/
292 gsl_sf_erfc_e
293 gsl_sf_erfc
294 gsl_sf_log_erfc_e
295 gsl_sf_log_erfc
296 gsl_sf_erf_e
297 gsl_sf_erf
298 gsl_sf_erf_Z_e
299 gsl_sf_erf_Q_e
300 gsl_sf_erf_Z
301 gsl_sf_erf_Q
302 gsl_sf_hazard_e
303 gsl_sf_hazard
305 push @EXPORT_misc, qw/
306 gsl_sf_exp_e
307 gsl_sf_exp
308 gsl_sf_exp_e10_e
309 gsl_sf_exp_mult_e
310 gsl_sf_exp_mult
311 gsl_sf_exp_mult_e10_e
312 gsl_sf_expm1_e
313 gsl_sf_expm1
314 gsl_sf_exprel_e
315 gsl_sf_exprel
316 gsl_sf_exprel_2_e
317 gsl_sf_exprel_2
318 gsl_sf_exprel_n_e
319 gsl_sf_exprel_n
320 gsl_sf_exp_err_e
321 gsl_sf_exp_err_e10_e
322 gsl_sf_exp_mult_err_e
323 gsl_sf_exp_mult_err_e10_e
324 gsl_sf_expint_E1_e
325 gsl_sf_expint_E1
326 gsl_sf_expint_E2_e
327 gsl_sf_expint_E2
328 gsl_sf_expint_En_e
329 gsl_sf_expint_En
330 gsl_sf_expint_E1_scaled_e
331 gsl_sf_expint_E1_scaled
332 gsl_sf_expint_E2_scaled_e
333 gsl_sf_expint_E2_scaled
334 gsl_sf_expint_En_scaled_e
335 gsl_sf_expint_En_scaled
336 gsl_sf_expint_Ei_e
337 gsl_sf_expint_Ei
338 gsl_sf_expint_Ei_scaled_e
339 gsl_sf_expint_Ei_scaled
340 gsl_sf_Shi_e
341 gsl_sf_Shi
342 gsl_sf_Chi_e
343 gsl_sf_Chi
344 gsl_sf_expint_3_e
345 gsl_sf_expint_3
346 gsl_sf_Si_e
347 gsl_sf_Si
348 gsl_sf_Ci_e
349 gsl_sf_Ci
351 @EXPORT_fermi_dirac = qw/
352 gsl_sf_fermi_dirac_m1_e
353 gsl_sf_fermi_dirac_m1
354 gsl_sf_fermi_dirac_0_e
355 gsl_sf_fermi_dirac_0
356 gsl_sf_fermi_dirac_1_e
357 gsl_sf_fermi_dirac_1
358 gsl_sf_fermi_dirac_2_e
359 gsl_sf_fermi_dirac_2
360 gsl_sf_fermi_dirac_int_e
361 gsl_sf_fermi_dirac_int
362 gsl_sf_fermi_dirac_mhalf_e
363 gsl_sf_fermi_dirac_mhalf
364 gsl_sf_fermi_dirac_half_e
365 gsl_sf_fermi_dirac_half
366 gsl_sf_fermi_dirac_3half_e
367 gsl_sf_fermi_dirac_3half
368 gsl_sf_fermi_dirac_inc_0_e
369 gsl_sf_fermi_dirac_inc_0
371 @EXPORT_legendre = qw/
372 gsl_sf_legendre_Pl_e
373 gsl_sf_legendre_Pl
374 gsl_sf_legendre_Pl_array
375 gsl_sf_legendre_Pl_deriv_array
376 gsl_sf_legendre_P1_e
377 gsl_sf_legendre_P2_e
378 gsl_sf_legendre_P3_e
379 gsl_sf_legendre_P1
380 gsl_sf_legendre_P2
381 gsl_sf_legendre_P3
382 gsl_sf_legendre_Q0_e
383 gsl_sf_legendre_Q0
384 gsl_sf_legendre_Q1_e
385 gsl_sf_legendre_Q1
386 gsl_sf_legendre_Ql_e
387 gsl_sf_legendre_Ql
388 gsl_sf_legendre_Plm_e
389 gsl_sf_legendre_Plm
390 gsl_sf_legendre_Plm_array
391 gsl_sf_legendre_Plm_deriv_array
392 gsl_sf_legendre_sphPlm_e
393 gsl_sf_legendre_sphPlm
394 gsl_sf_legendre_sphPlm_array
395 gsl_sf_legendre_sphPlm_deriv_array
396 gsl_sf_legendre_array_size
397 gsl_sf_legendre_H3d_0_e
398 gsl_sf_legendre_H3d_0
399 gsl_sf_legendre_H3d_1_e
400 gsl_sf_legendre_H3d_1
401 gsl_sf_legendre_H3d_e
402 gsl_sf_legendre_H3d
403 gsl_sf_legendre_H3d_array
405 @EXPORT_gamma = qw/
406 gsl_sf_lngamma_e
407 gsl_sf_lngamma
408 gsl_sf_lngamma_sgn_e
409 gsl_sf_gamma_e
410 gsl_sf_gamma
411 gsl_sf_gammastar_e
412 gsl_sf_gammastar
413 gsl_sf_gammainv_e
414 gsl_sf_gammainv
415 gsl_sf_lngamma_complex_e
416 gsl_sf_gamma_inc_Q_e
417 gsl_sf_gamma_inc_Q
418 gsl_sf_gamma_inc_P_e
419 gsl_sf_gamma_inc_P
420 gsl_sf_gamma_inc_e
421 gsl_sf_gamma_inc
423 @EXPORT_factorial = qw/
424 gsl_sf_fact_e
425 gsl_sf_fact
426 gsl_sf_doublefact_e
427 gsl_sf_doublefact
428 gsl_sf_lnfact_e
429 gsl_sf_lnfact
430 gsl_sf_lndoublefact_e
431 gsl_sf_lndoublefact
433 @EXPORT_hypergeometric = qw/
434 gsl_sf_hyperg_0F1_e
435 gsl_sf_hyperg_0F1
436 gsl_sf_hyperg_1F1_int_e
437 gsl_sf_hyperg_1F1_int
438 gsl_sf_hyperg_1F1_e
439 gsl_sf_hyperg_1F1
440 gsl_sf_hyperg_U_int_e
441 gsl_sf_hyperg_U_int
442 gsl_sf_hyperg_U_int_e10_e
443 gsl_sf_hyperg_U_e
444 gsl_sf_hyperg_U
445 gsl_sf_hyperg_U_e10_e
446 gsl_sf_hyperg_2F1_e
447 gsl_sf_hyperg_2F1
448 gsl_sf_hyperg_2F1_conj_e
449 gsl_sf_hyperg_2F1_conj
450 gsl_sf_hyperg_2F1_renorm_e
451 gsl_sf_hyperg_2F1_renorm
452 gsl_sf_hyperg_2F1_conj_renorm_e
453 gsl_sf_hyperg_2F1_conj_renorm
454 gsl_sf_hyperg_2F0_e
455 gsl_sf_hyperg_2F0
457 @EXPORT_laguerre = qw/
458 gsl_sf_laguerre_1_e
459 gsl_sf_laguerre_2_e
460 gsl_sf_laguerre_3_e
461 gsl_sf_laguerre_1
462 gsl_sf_laguerre_2
463 gsl_sf_laguerre_3
464 gsl_sf_laguerre_n_e
465 gsl_sf_laguerre_n
467 push @EXPORT_misc, qw/
468 gsl_sf_taylorcoeff_e
469 gsl_sf_taylorcoeff
470 gsl_sf_lnchoose_e
471 gsl_sf_lnchoose
472 gsl_sf_choose_e
473 gsl_sf_choose
474 gsl_sf_lnpoch_e
475 gsl_sf_lnpoch
476 gsl_sf_lnpoch_sgn_e
477 gsl_sf_poch_e
478 gsl_sf_poch
479 gsl_sf_pochrel_e
480 gsl_sf_pochrel
481 gsl_sf_lnbeta_e
482 gsl_sf_lnbeta
483 gsl_sf_lnbeta_sgn_e
484 gsl_sf_beta_e
485 gsl_sf_beta
486 gsl_sf_beta_inc_e
487 gsl_sf_beta_inc
488 gsl_sf_gegenpoly_1_e
489 gsl_sf_gegenpoly_2_e
490 gsl_sf_gegenpoly_3_e
491 gsl_sf_gegenpoly_1
492 gsl_sf_gegenpoly_2
493 gsl_sf_gegenpoly_3
494 gsl_sf_gegenpoly_n_e
495 gsl_sf_gegenpoly_n
496 gsl_sf_gegenpoly_array
497 gsl_sf_lambert_W0_e
498 gsl_sf_lambert_W0
499 gsl_sf_lambert_Wm1_e
500 gsl_sf_lambert_Wm1
501 gsl_sf_conicalP_half_e
502 gsl_sf_conicalP_half
503 gsl_sf_conicalP_mhalf_e
504 gsl_sf_conicalP_mhalf
505 gsl_sf_conicalP_0_e
506 gsl_sf_conicalP_0
507 gsl_sf_conicalP_1_e
508 gsl_sf_conicalP_1
509 gsl_sf_conicalP_sph_reg_e
510 gsl_sf_conicalP_sph_reg
511 gsl_sf_conicalP_cyl_reg_e
512 gsl_sf_conicalP_cyl_reg
513 gsl_sf_log_e
514 gsl_sf_log
515 gsl_sf_log_abs_e
516 gsl_sf_log_abs
517 gsl_sf_complex_log_e
518 gsl_sf_log_1plusx_e
519 gsl_sf_log_1plusx
520 gsl_sf_log_1plusx_mx_e
521 gsl_sf_log_1plusx_mx
522 gsl_sf_pow_int_e
523 gsl_sf_pow_int
524 gsl_sf_psi_int_e
525 gsl_sf_psi_int
526 gsl_sf_psi_e
527 gsl_sf_psi
528 gsl_sf_psi_1piy_e
529 gsl_sf_psi_1piy
530 gsl_sf_complex_psi_e
531 gsl_sf_psi_1_int_e
532 gsl_sf_psi_1_int
533 gsl_sf_psi_1_e
534 gsl_sf_psi_1
535 gsl_sf_psi_n_e
536 gsl_sf_psi_n
537 gsl_sf_result_smash_e
538 gsl_sf_synchrotron_1_e
539 gsl_sf_synchrotron_1
540 gsl_sf_synchrotron_2_e
541 gsl_sf_synchrotron_2
543 @EXPORT_mathieu = qw/
544 gsl_sf_mathieu_a_array
545 gsl_sf_mathieu_b_array
546 gsl_sf_mathieu_a
547 gsl_sf_mathieu_b
548 gsl_sf_mathieu_a_coeff
549 gsl_sf_mathieu_b_coeff
550 gsl_sf_mathieu_alloc
551 gsl_sf_mathieu_free
552 gsl_sf_mathieu_ce
553 gsl_sf_mathieu_se
554 gsl_sf_mathieu_ce_array
555 gsl_sf_mathieu_se_array
556 gsl_sf_mathieu_Mc
557 gsl_sf_mathieu_Ms
558 gsl_sf_mathieu_Mc_array
559 gsl_sf_mathieu_Ms_array
561 @EXPORT_transport = qw/
562 gsl_sf_transport_2_e
563 gsl_sf_transport_2
564 gsl_sf_transport_3_e
565 gsl_sf_transport_3
566 gsl_sf_transport_4_e
567 gsl_sf_transport_4
568 gsl_sf_transport_5_e
569 gsl_sf_transport_5
571 @EXPORT_trig = qw/
572 gsl_sf_sin_e
573 gsl_sf_sin
574 gsl_sf_sin_pi_x_e
575 gsl_sf_cos_e
576 gsl_sf_cos_pi_x_e
577 gsl_sf_cos
578 gsl_sf_hypot_e
579 gsl_sf_hypot
580 gsl_sf_complex_sin_e
581 gsl_sf_complex_cos_e
582 gsl_sf_complex_logsin_e
583 gsl_sf_sinc_e
584 gsl_sf_sinc
585 gsl_sf_lnsinh_e
586 gsl_sf_lnsinh
587 gsl_sf_lncosh_e
588 gsl_sf_lncosh
589 gsl_sf_polar_to_rect
590 gsl_sf_rect_to_polar
591 gsl_sf_sin_err_e
592 gsl_sf_cos_err_e
593 gsl_sf_angle_restrict_symm_e
594 gsl_sf_angle_restrict_symm
595 gsl_sf_angle_restrict_pos_e
596 gsl_sf_angle_restrict_pos
597 gsl_sf_angle_restrict_symm_err_e
598 gsl_sf_angle_restrict_pos_err_e
599 gsl_sf_atanint_e
600 gsl_sf_atanint
602 @EXPORT_zeta = qw/
603 gsl_sf_zeta_int_e
604 gsl_sf_zeta_int
605 gsl_sf_zeta_e
606 gsl_sf_zeta
607 gsl_sf_zetam1_e
608 gsl_sf_zetam1
609 gsl_sf_zetam1_int_e
610 gsl_sf_zetam1_int
611 gsl_sf_hzeta_e
612 gsl_sf_hzeta
614 @EXPORT_eta = qw/
615 gsl_sf_eta_int_e
616 gsl_sf_eta_int
617 gsl_sf_eta_e
618 gsl_sf_eta
620 @EXPORT_vars = qw/
621 GSL_SF_GAMMA_XMAX
622 GSL_SF_FACT_NMAX
623 GSL_SF_DOUBLEFACT_NMAX
624 GSL_SF_MATHIEU_COEFF
627 @EXPORT_OK = (
628 @EXPORT_airy, @EXPORT_bessel, @EXPORT_clausen, @EXPORT_hydrogenic,
629 @EXPORT_coulumb, @EXPORT_coupling, @EXPORT_dawson, @EXPORT_debye,
630 @EXPORT_dilog, @EXPORT_misc, @EXPORT_elliptic, @EXPORT_error, @EXPORT_legendre,
631 @EXPORT_gamma, @EXPORT_transport, @EXPORT_trig, @EXPORT_zeta, @EXPORT_eta,
632 @EXPORT_vars
635 %EXPORT_TAGS = (
636 all => [ @EXPORT_OK ],
637 airy => [ @EXPORT_airy ],
638 bessel => [ @EXPORT_bessel ],
639 clausen => [ @EXPORT_clausen ],
640 coulumb => [ @EXPORT_coulumb ],
641 coupling => [ @EXPORT_coupling ],
642 dawson => [ @EXPORT_dawson ],
643 debye => [ @EXPORT_debye ],
644 dilog => [ @EXPORT_dilog ],
645 eta => [ @EXPORT_eta ],
646 elliptic => [ @EXPORT_elliptic ],
647 error => [ @EXPORT_error ],
648 factorial => [ @EXPORT_factorial ],
649 gamma => [ @EXPORT_gamma ],
650 hydrogenic => [ @EXPORT_hydrogenic ],
651 hypergeometric => [ @EXPORT_hypergeometric ],
652 laguerre => [ @EXPORT_laguerre ],
653 legendre => [ @EXPORT_legendre ],
654 mathieu => [ @EXPORT_mathieu ],
655 misc => [ @EXPORT_misc ],
656 transport => [ @EXPORT_transport ],
657 trig => [ @EXPORT_trig ],
658 vars => [ @EXPORT_vars ],
659 zeta => [ @EXPORT_zeta ],
662 __END__
664 =head1 NAME
666 Math::GSL::SF - Special Functions
668 =head1 SYNOPSIS
670 use Math::GSL::SF qw /:all/;
672 =head1 DESCRIPTION
674 This module contains a data structure named gsl_sf_result. To create a new one use
676 $r = Math::GSL::SF::gsl_sf_result_struct->new;
678 You can then access the elements of the structure in this way :
680 my $val = $r->{val};
682 my $error = $r->{err};
684 Here is a list of all included functions:
686 =over
688 =item C<gsl_sf_airy_Ai_e($x, $mode)>
690 =item C<gsl_sf_airy_Ai($x, $mode, $result)>
692 - These routines compute the Airy function Ai($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
694 =back
696 =over
698 =item C<gsl_sf_airy_Bi_e($x, $mode, $result)>
700 =item C<gsl_sf_airy_Bi($x, $mode)>
702 - These routines compute the Airy function Bi($x) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
704 =back
706 =over
708 =item C<gsl_sf_airy_Ai_scaled_e($x, $mode, $result)>
710 =item C<gsl_sf_airy_Ai_scaled($x, $mode)>
712 - These routines compute a scaled version of the Airy function S_A($x) Ai($x). For $x>0 the scaling factor S_A($x) is \exp(+(2/3) $x**(3/2)), and is 1 for $x<0. $result is a gsl_sf_result structure.
714 =back
716 =over
718 =item C<gsl_sf_airy_Bi_scaled_e($x, $mode, $result)>
720 =item C<gsl_sf_airy_Bi_scaled($x, $mode)>
722 - These routines compute a scaled version of the Airy function S_B($x) Bi($x). For $x>0 the scaling factor S_B($x) is exp(-(2/3) $x**(3/2)), and is 1 for $x<0. $result is a gsl_sf_result structure.
724 =back
726 =over
728 =item C<gsl_sf_airy_Ai_deriv_e($x, $mode, $result)>
730 =item C<gsl_sf_airy_Ai_deriv($x, $mode)>
732 - These routines compute the Airy function derivative Ai'($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure.
734 =back
736 =over
738 =item C<gsl_sf_airy_Bi_deriv_e($x, $mode, $result)>
740 =item C<gsl_sf_airy_Bi_deriv($x, $mode)>
742 -These routines compute the Airy function derivative Bi'($x) with an accuracy specified by $mode. $result is a gsl_sf_result structure.
744 =back
746 =over
748 =item C<gsl_sf_airy_Ai_deriv_scaled_e($x, $mode, $result)>
750 =item C<gsl_sf_airy_Ai_deriv_scaled($x, $mode)>
752 -These routines compute the scaled Airy function derivative S_A(x) Ai'(x). For x>0 the scaling factor S_A(x) is \exp(+(2/3) x^(3/2)), and is 1 for x<0. $result is a gsl_sf_result structure.
754 =back
756 =over
758 =item C<gsl_sf_airy_Bi_deriv_scaled_e($x, $mode, $result)>
760 =item C<gsl_sf_airy_Bi_deriv_scaled($x, $mode)>
762 -These routines compute the scaled Airy function derivative S_B(x) Bi'(x). For x>0 the scaling factor S_B(x) is exp(-(2/3) x^(3/2)), and is 1 for x<0. $result is a gsl_sf_result structure.
764 =back
766 =over
768 =item C<gsl_sf_airy_zero_Ai_e($s, $result)>
770 =item C<gsl_sf_airy_zero_Ai($s)>
772 -These routines compute the location of the s-th zero of the Airy function Ai($x). $result is a gsl_sf_result structure.
774 =back
776 =over
778 =item C<gsl_sf_airy_zero_Bi_e($s, $result)>
780 =item C<gsl_sf_airy_zero_Bi($s)>
782 -These routines compute the location of the s-th zero of the Airy function Bi($x). $result is a gsl_sf_result structure.
784 =back
786 =over
788 =item C<gsl_sf_airy_zero_Ai_deriv_e($s, $result)>
790 =item C<gsl_sf_airy_zero_Ai_deriv($s)>
792 -These routines compute the location of the s-th zero of the Airy function derivative Ai'(x). $result is a gsl_sf_result structure.
794 =back
796 =over
798 =item C<gsl_sf_airy_zero_Bi_deriv_e($s, $result)>
800 =item C<gsl_sf_airy_zero_Bi_deriv($s)>
802 - These routines compute the location of the s-th zero of the Airy function derivative Bi'(x). $result is a gsl_sf_result structure.
804 =back
806 =over
808 =item C<gsl_sf_bessel_J0_e($x, $result)>
810 =item C<gsl_sf_bessel_J0($x)>
812 -These routines compute the regular cylindrical Bessel function of zeroth order, J_0($x). $result is a gsl_sf_result structure.
814 =back
816 =over
818 =item C<gsl_sf_bessel_J1_e($x, $result)>
820 =item C<gsl_sf_bessel_J1($x)>
822 - These routines compute the regular cylindrical Bessel function of first order, J_1($x). $result is a gsl_sf_result structure.
824 =back
826 =over
828 =item C<gsl_sf_bessel_Jn_e($n, $x, $result)>
830 =item C<gsl_sf_bessel_Jn($n, $x)>
832 -These routines compute the regular cylindrical Bessel function of order n, J_n($x).
834 =back
836 =over
838 =item C<gsl_sf_bessel_Jn_array($nmin, $nmax, $x, $result_array)> - This routine computes the values of the regular cylindrical Bessel functions J_n($x) for n from $nmin to $nmax inclusive, storing the results in the array $result_array. The values are computed using recurrence relations for efficiency, and therefore may differ slightly from the exact values.
840 =back
842 =over
844 =item C<gsl_sf_bessel_Y0_e>
846 =item C<gsl_sf_bessel_Y0>
850 =back
852 =over
854 =item C<gsl_sf_bessel_Y1_e>
856 =item C<gsl_sf_bessel_Y1>
860 =back
862 =over
864 =item C<gsl_sf_bessel_Yn_e>
866 =item C<gsl_sf_bessel_Yn>
870 =back
872 =over
874 =item C<gsl_sf_bessel_Yn_array>
878 =back
880 =over
882 =item C<gsl_sf_bessel_I0_e >
884 =item C<gsl_sf_bessel_I0>
888 =back
890 =over
892 =item C<gsl_sf_bessel_I1_e>
894 =item C<gsl_sf_bessel_I1>
898 =back
900 =over
902 =item C<gsl_sf_bessel_In_e>
904 =item C<gsl_sf_bessel_In>
908 =back
910 =over
912 =item C<gsl_sf_bessel_In_array>
916 =back
918 =over
920 =item C<gsl_sf_bessel_I0_scaled_e>
922 =item C<gsl_sf_bessel_I0_scaled>
926 =back
928 =over
930 =item C<gsl_sf_bessel_I1_scaled_e>
932 =item C<gsl_sf_bessel_I1_scaled>
936 =back
938 =over
940 =item C<gsl_sf_bessel_In_scaled_e>
942 =item C<gsl_sf_bessel_In_scaled >
946 =back
948 =over
950 =item C<gsl_sf_bessel_In_scaled_array>
954 =back
956 =over
958 =item C<gsl_sf_bessel_K0_e>
960 =item C<gsl_sf_bessel_K0 >
964 =back
966 =over
968 =item C<gsl_sf_bessel_K1_e>
970 =item C<gsl_sf_bessel_K1>
974 =back
976 =over
978 =item C<gsl_sf_bessel_Kn_e>
980 =item C<gsl_sf_bessel_Kn>
984 =back
986 =over
988 =item C<gsl_sf_bessel_Kn_array>
992 =back
994 =over
996 =item C<gsl_sf_bessel_K0_scaled_e >
998 =item C<gsl_sf_bessel_K0_scaled>
1002 =back
1004 =over
1006 =item C<gsl_sf_bessel_K1_scaled_e>
1008 =item C<gsl_sf_bessel_K1_scaled >
1012 =back
1014 =over
1016 =item C<gsl_sf_bessel_Kn_scaled_e>
1018 =item C<gsl_sf_bessel_Kn_scaled>
1022 =back
1024 =over
1026 =item C<gsl_sf_bessel_Kn_scaled_array >
1030 =back
1032 =over
1034 =item C<gsl_sf_bessel_j0_e>
1036 =item C<gsl_sf_bessel_j0>
1040 =back
1042 =over
1044 =item C<gsl_sf_bessel_j1_e >
1046 =item C<gsl_sf_bessel_j1>
1050 =back
1052 =over
1054 =item C<gsl_sf_bessel_j2_e>
1056 =item C<gsl_sf_bessel_j2>
1060 =back
1062 =over
1064 =item C<gsl_sf_bessel_jl_e>
1066 =item C<gsl_sf_bessel_jl>
1070 =back
1072 =over
1074 =item C<gsl_sf_bessel_jl_array>
1078 =back
1080 =over
1082 =item C<gsl_sf_bessel_jl_steed_array>
1086 =back
1088 =over
1090 =item C<gsl_sf_bessel_y0_e>
1092 =item C<gsl_sf_bessel_y0 >
1096 =back
1098 =over
1100 =item C<gsl_sf_bessel_y1_e>
1102 =item C<gsl_sf_bessel_y1>
1106 =back
1108 =over
1110 =item C<gsl_sf_bessel_y2_e >
1112 =item C<gsl_sf_bessel_y2>
1116 =back
1118 =over
1120 =item C<gsl_sf_bessel_yl_e>
1122 =item C<gsl_sf_bessel_yl >
1126 =back
1128 =over
1130 =item C<gsl_sf_bessel_yl_array>
1134 =back
1136 =over
1138 =item C<gsl_sf_bessel_i0_scaled_e>
1140 =item C<gsl_sf_bessel_i0_scaled>
1144 =back
1146 =over
1148 =item C<gsl_sf_bessel_i1_scaled_e>
1150 =item C<gsl_sf_bessel_i1_scaled>
1154 =back
1156 =over
1158 =item C<gsl_sf_bessel_i2_scaled_e>
1160 =item C<gsl_sf_bessel_i2_scaled>
1164 =back
1166 =over
1168 =item C<gsl_sf_bessel_il_scaled_e>
1170 =item C<gsl_sf_bessel_il_scaled>
1174 =back
1176 =over
1178 =item C<gsl_sf_bessel_il_scaled_array>
1182 =back
1184 =over
1186 =item C<gsl_sf_bessel_k0_scaled_e>
1188 =item C<gsl_sf_bessel_k0_scaled >
1192 =back
1194 =over
1196 =item C<gsl_sf_bessel_k1_scaled_e>
1198 =item C<gsl_sf_bessel_k1_scaled>
1202 =back
1204 =over
1206 =item C<gsl_sf_bessel_k2_scaled_e >
1208 =item C<gsl_sf_bessel_k2_scaled>
1212 =back
1214 =over
1216 =item C<gsl_sf_bessel_kl_scaled_e>
1218 =item C<gsl_sf_bessel_kl_scaled>
1222 =back
1224 =over
1226 =item C<gsl_sf_bessel_kl_scaled_array>
1230 =back
1232 =over
1234 =item C<gsl_sf_bessel_Jnu_e>
1236 =item C<gsl_sf_bessel_Jnu >
1240 =back
1242 =over
1244 =item C<gsl_sf_bessel_Ynu_e>
1246 =item C<gsl_sf_bessel_Ynu>
1250 =back
1252 =over
1254 =item C<gsl_sf_bessel_sequence_Jnu_e >
1258 =back
1260 =over
1262 =item C<gsl_sf_bessel_Inu_scaled_e>
1264 =item C<gsl_sf_bessel_Inu_scaled>
1268 =back
1270 =over
1272 =item C<gsl_sf_bessel_Inu_e >
1274 =item C<gsl_sf_bessel_Inu>
1278 =back
1280 =over
1282 =item C<gsl_sf_bessel_Knu_scaled_e>
1284 =item C<gsl_sf_bessel_Knu_scaled >
1288 =back
1290 =over
1292 =item C<gsl_sf_bessel_Knu_e>
1294 =item C<gsl_sf_bessel_Knu>
1298 =back
1300 =over
1302 =item C<gsl_sf_bessel_lnKnu_e >
1304 =item C<gsl_sf_bessel_lnKnu>
1308 =back
1310 =over
1312 =item C<gsl_sf_bessel_zero_J0_e>
1314 =item C<gsl_sf_bessel_zero_J0 >
1318 =back
1320 =over
1322 =item C<gsl_sf_bessel_zero_J1_e>
1324 =item C<gsl_sf_bessel_zero_J1>
1328 =back
1330 =over
1332 =item C<gsl_sf_bessel_zero_Jnu_e>
1334 =item C<gsl_sf_bessel_zero_Jnu>
1338 =back
1340 =over
1342 =item C<gsl_sf_clausen_e>
1344 =item C<gsl_sf_clausen >
1348 =back
1350 =over
1352 =item C<gsl_sf_hydrogenicR_1_e>
1354 =item C<gsl_sf_hydrogenicR_1>
1358 =back
1360 =over
1362 =item C<gsl_sf_hydrogenicR_e >
1364 =item C<gsl_sf_hydrogenicR>
1368 =back
1370 =over
1372 =item C<gsl_sf_coulomb_wave_FG_e> -
1374 =item C<gsl_sf_coulomb_wave_F_array > -
1376 =item C<gsl_sf_coulomb_wave_FG_array> -
1378 =item C<gsl_sf_coulomb_wave_FGp_array> -
1380 =item C<gsl_sf_coulomb_wave_sphF_array> -
1382 =item C<gsl_sf_coulomb_CL_e> -
1384 =item C<gsl_sf_coulomb_CL_arrayi> -
1386 =item C<gsl_sf_coupling_3j_e>
1388 =item C<gsl_sf_coupling_3j>
1392 =back
1394 =over
1396 =item C<gsl_sf_coupling_6j_e>
1398 =item C<gsl_sf_coupling_6j>
1402 =back
1404 =over
1406 =item C<gsl_sf_coupling_RacahW_e>
1408 =item C<gsl_sf_coupling_RacahW>
1412 =back
1414 =over
1416 =item C<gsl_sf_coupling_9j_e>
1418 =item C<gsl_sf_coupling_9j>
1422 =back
1424 =over
1426 =item C<gsl_sf_dawson_e>
1428 =item C<gsl_sf_dawson>
1432 =back
1434 =over
1436 =item C<gsl_sf_debye_1_e>
1438 =item C<gsl_sf_debye_1>
1442 =back
1444 =over
1446 =item C<gsl_sf_debye_2_e>
1448 =item C<gsl_sf_debye_2 >
1452 =back
1454 =over
1456 =item C<gsl_sf_debye_3_e>
1458 =item C<gsl_sf_debye_3>
1462 =back
1464 =over
1466 =item C<gsl_sf_debye_4_e>
1468 =item C<gsl_sf_debye_4>
1472 =back
1474 =over
1476 =item C<gsl_sf_debye_5_e>
1478 =item C<gsl_sf_debye_5 >
1482 =back
1484 =over
1486 =item C<gsl_sf_debye_6_e>
1488 =item C<gsl_sf_debye_6>
1492 =back
1494 =over
1496 =item C<gsl_sf_dilog_e >
1498 =item C<gsl_sf_dilog>
1502 =back
1504 =over
1506 =item C<gsl_sf_complex_dilog_xy_e> -
1508 =item C<gsl_sf_complex_dilog_e > -
1510 =item C<gsl_sf_complex_spence_xy_e> -
1512 =item C<gsl_sf_multiply_e> -
1514 =item C<gsl_sf_multiply> -
1516 =item C<gsl_sf_multiply_err_e> -
1518 =item C<gsl_sf_ellint_Kcomp_e>
1520 =item C<gsl_sf_ellint_Kcomp>
1524 =back
1526 =over
1528 =item C<gsl_sf_ellint_Ecomp_e>
1530 =item C<gsl_sf_ellint_Ecomp>
1534 =back
1536 =over
1538 =item C<gsl_sf_ellint_Pcomp_e >
1540 =item C<gsl_sf_ellint_Pcomp>
1544 =back
1546 =over
1548 =item C<gsl_sf_ellint_Dcomp_e>
1550 =item C<gsl_sf_ellint_Dcomp >
1554 =back
1556 =over
1558 =item C<gsl_sf_ellint_F_e>
1560 =item C<gsl_sf_ellint_F>
1564 =back
1566 =over
1568 =item C<gsl_sf_ellint_E_e>
1570 =item C<gsl_sf_ellint_E>
1574 =back
1576 =over
1578 =item C<gsl_sf_ellint_P_e>
1580 =item C<gsl_sf_ellint_P>
1584 =back
1586 =over
1588 =item C<gsl_sf_ellint_D_e>
1590 =item C<gsl_sf_ellint_D>
1594 =back
1596 =over
1598 =item C<gsl_sf_ellint_RC_e >
1600 =item C<gsl_sf_ellint_RC>
1604 =back
1606 =over
1608 =item C<gsl_sf_ellint_RD_e>
1610 =item C<gsl_sf_ellint_RD >
1614 =back
1616 =over
1618 =item C<gsl_sf_ellint_RF_e>
1620 =item C<gsl_sf_ellint_RF>
1624 =back
1626 =over
1628 =item C<gsl_sf_ellint_RJ_e >
1630 =item C<gsl_sf_ellint_RJ>
1634 =back
1636 =over
1638 =item C<gsl_sf_elljac_e> -
1640 =item C<gsl_sf_erfc_e >
1642 =item C<gsl_sf_erfc>
1646 =back
1648 =over
1650 =item C<gsl_sf_log_erfc_e>
1652 =item C<gsl_sf_log_erfc >
1656 =back
1658 =over
1660 =item C<gsl_sf_erf_e>
1662 =item C<gsl_sf_erf>
1666 =back
1668 =over
1670 =item C<gsl_sf_erf_Z_e >
1672 =item C<gsl_sf_erf_Z>
1676 =back
1678 =over
1680 =item C<gsl_sf_erf_Q_e>
1682 =item C<gsl_sf_erf_Q >
1686 =back
1688 =over
1690 =item C<gsl_sf_hazard_e>
1692 =item C<gsl_sf_hazard>
1696 =back
1698 =over
1700 =item C<gsl_sf_exp_e >
1702 =item C<gsl_sf_exp>
1706 =back
1708 =over
1710 =item C<gsl_sf_exp_e10_e> -
1712 =item C<gsl_sf_exp_mult_e >
1714 =item C<gsl_sf_exp_mult>
1718 =back
1720 =over
1722 =item C<gsl_sf_exp_mult_e10_e> -
1724 =item C<gsl_sf_expm1_e >
1726 =item C<gsl_sf_expm1>
1730 =back
1732 =over
1734 =item C<gsl_sf_exprel_e>
1736 =item C<gsl_sf_exprel >
1740 =back
1742 =over
1744 =item C<gsl_sf_exprel_2_e>
1746 =item C<gsl_sf_exprel_2>
1750 =back
1752 =over
1754 =item C<gsl_sf_exprel_n_e >
1756 =item C<gsl_sf_exprel_n>
1760 =back
1762 =over
1764 =item C<gsl_sf_exp_err_e> -
1766 =item C<gsl_sf_exp_err_e10_e > -
1768 =item C<gsl_sf_exp_mult_err_e> -
1770 =item C<gsl_sf_exp_mult_err_e10_e> -
1772 =item C<gsl_sf_expint_E1_e >
1774 =item C<gsl_sf_expint_E1>
1778 =back
1780 =over
1782 =item C<gsl_sf_expint_E2_e>
1784 =item C<gsl_sf_expint_E2 >
1788 =back
1790 =over
1792 =item C<gsl_sf_expint_En_e>
1794 =item C<gsl_sf_expint_En>
1798 =back
1800 =over
1802 =item C<gsl_sf_expint_E1_scaled_e >
1804 =item C<gsl_sf_expint_E1_scaled>
1808 =back
1810 =over
1812 =item C<gsl_sf_expint_E2_scaled_e>
1814 =item C<gsl_sf_expint_E2_scaled >
1818 =back
1820 =over
1822 =item C<gsl_sf_expint_En_scaled_e>
1824 =item C<gsl_sf_expint_En_scaled>
1828 =back
1830 =over
1832 =item C<gsl_sf_expint_Ei_e >
1834 =item C<gsl_sf_expint_Ei>
1838 =back
1840 =over
1842 =item C<gsl_sf_expint_Ei_scaled_e>
1844 =item C<gsl_sf_expint_Ei_scaled >
1848 =back
1850 =over
1852 =item C<gsl_sf_Shi_e>
1854 =item C<gsl_sf_Shi>
1858 =back
1860 =over
1862 =item C<gsl_sf_Chi_e >
1864 =item C<gsl_sf_Chi>
1868 =back
1870 =over
1872 =item C<gsl_sf_expint_3_e>
1874 =item C<gsl_sf_expint_3 >
1878 =back
1880 =over
1882 =item C<gsl_sf_Si_e>
1884 =item C<gsl_sf_Si>
1888 =back
1890 =over
1892 =item C<gsl_sf_Ci_e >
1894 =item C<gsl_sf_Ci>
1898 =back
1900 =over
1902 =item C<gsl_sf_fermi_dirac_m1_e>
1904 =item C<gsl_sf_fermi_dirac_m1 >
1908 =back
1910 =over
1912 =item C<gsl_sf_fermi_dirac_0_e>
1914 =item C<gsl_sf_fermi_dirac_0>
1918 =back
1920 =over
1922 =item C<gsl_sf_fermi_dirac_1_e >
1924 =item C<gsl_sf_fermi_dirac_1>
1928 =back
1930 =over
1932 =item C<gsl_sf_fermi_dirac_2_e>
1934 =item C<gsl_sf_fermi_dirac_2 >
1938 =back
1940 =over
1942 =item C<gsl_sf_fermi_dirac_int_e>
1944 =item C<gsl_sf_fermi_dirac_int>
1948 =back
1950 =over
1952 =item C<gsl_sf_fermi_dirac_mhalf_e >
1954 =item C<gsl_sf_fermi_dirac_mhalf>
1958 =back
1960 =over
1962 =item C<gsl_sf_fermi_dirac_half_e>
1964 =item C<gsl_sf_fermi_dirac_half >
1968 =back
1970 =over
1972 =item C<gsl_sf_fermi_dirac_3half_e>
1974 =item C<gsl_sf_fermi_dirac_3half>
1978 =back
1980 =over
1982 =item C<gsl_sf_fermi_dirac_inc_0_e >
1984 =item C<gsl_sf_fermi_dirac_inc_0>
1988 =back
1990 =over
1992 =item C<gsl_sf_legendre_Pl_e>
1994 =item C<gsl_sf_legendre_Pl >
1998 =back
2000 =over
2002 =item C<gsl_sf_legendre_Pl_array>
2004 =item C<gsl_sf_legendre_Pl_deriv_array>
2008 =back
2010 =over
2012 =item C<gsl_sf_legendre_P1_e >
2014 =item C<gsl_sf_legendre_P2_e>
2016 =item C<gsl_sf_legendre_P3_e>
2018 =item C<gsl_sf_legendre_P1 >
2020 =item C<gsl_sf_legendre_P2>
2022 =item C<gsl_sf_legendre_P3>
2026 =back
2028 =over
2030 =item C<gsl_sf_legendre_Q0_e >
2032 =item C<gsl_sf_legendre_Q0>
2036 =back
2038 =over
2040 =item C<gsl_sf_legendre_Q1_e>
2042 =item C<gsl_sf_legendre_Q1 >
2046 =back
2048 =over
2050 =item C<gsl_sf_legendre_Ql_e>
2052 =item C<gsl_sf_legendre_Ql>
2056 =back
2058 =over
2060 =item C<gsl_sf_legendre_Plm_e >
2062 =item C<gsl_sf_legendre_Plm>
2066 =back
2068 =over
2070 =item C<gsl_sf_legendre_Plm_array>
2072 =item C<gsl_sf_legendre_Plm_deriv_array >
2076 =back
2078 =over
2080 =item C<gsl_sf_legendre_sphPlm_e>
2082 =item C<gsl_sf_legendre_sphPlm>
2086 =back
2088 =over
2090 =item C<gsl_sf_legendre_sphPlm_array >
2092 =item C<gsl_sf_legendre_sphPlm_deriv_array>
2096 =back
2098 =over
2100 =item C<gsl_sf_legendre_array_size> -
2102 =item C<gsl_sf_lngamma_e >
2104 =item C<gsl_sf_lngamma>
2108 =back
2110 =over
2112 =item C<gsl_sf_lngamma_sgn_e>
2114 =item C<gsl_sf_gamma_e >
2116 =item C<gsl_sf_gamma>
2118 =item C<gsl_sf_gammastar_e>
2120 =item C<gsl_sf_gammastar >
2122 =item C<gsl_sf_gammainv_e>
2124 =item C<gsl_sf_gammainv>
2126 =item C<gsl_sf_lngamma_complex_e >
2128 =item C<gsl_sf_gamma_inc_Q_e>
2130 =item C<gsl_sf_gamma_inc_Q>
2132 =item C<gsl_sf_gamma_inc_P_e >
2134 =item C<gsl_sf_gamma_inc_P>
2136 =item C<gsl_sf_gamma_inc_e>
2138 =item C<gsl_sf_gamma_inc >
2140 =item C<gsl_sf_taylorcoeff_e>
2142 =item C<gsl_sf_taylorcoeff>
2144 =item C<gsl_sf_fact_e >
2146 =item C<gsl_sf_fact>
2148 =item C<gsl_sf_doublefact_e>
2150 =item C<gsl_sf_doublefact >
2152 =item C<gsl_sf_lnfact_e>
2154 =item C<gsl_sf_lnfact>
2156 =item C<gsl_sf_lndoublefact_e >
2158 =item C<gsl_sf_lndoublefact>
2160 =item C<gsl_sf_lnchoose_e>
2162 =item C<gsl_sf_lnchoose >
2164 =item C<gsl_sf_choose_e>
2166 =item C<gsl_sf_choose>
2168 =item C<gsl_sf_lnpoch_e >
2170 =item C<gsl_sf_lnpoch>
2172 =item C<gsl_sf_lnpoch_sgn_e>
2174 =item C<gsl_sf_poch_e >
2176 =item C<gsl_sf_poch>
2178 =item C<gsl_sf_pochrel_e>
2180 =item C<gsl_sf_pochrel >
2182 =item C<gsl_sf_lnbeta_e>
2184 =item C<gsl_sf_lnbeta>
2186 =item C<gsl_sf_lnbeta_sgn_e >
2188 =item C<gsl_sf_beta_e>
2190 =item C<gsl_sf_beta>
2192 =item C<gsl_sf_beta_inc_e >
2194 =item C<gsl_sf_beta_inc>
2196 =item C<gsl_sf_gegenpoly_1_e>
2198 =item C<gsl_sf_gegenpoly_2_e >
2200 =item C<gsl_sf_gegenpoly_3_e>
2202 =item C<gsl_sf_gegenpoly_1>
2204 =item C<gsl_sf_gegenpoly_2 >
2206 =item C<gsl_sf_gegenpoly_3>
2208 =item C<gsl_sf_gegenpoly_n_e>
2210 =item C<gsl_sf_gegenpoly_n >
2212 =item C<gsl_sf_gegenpoly_array>
2214 =item C<gsl_sf_hyperg_0F1_e>
2216 =item C<gsl_sf_hyperg_0F1 >
2218 =item C<gsl_sf_hyperg_1F1_int_e>
2220 =item C<gsl_sf_hyperg_1F1_int>
2222 =item C<gsl_sf_hyperg_1F1_e >
2224 =item C<gsl_sf_hyperg_1F1>
2226 =item C<gsl_sf_hyperg_U_int_e>
2228 =item C<gsl_sf_hyperg_U_int >
2230 =item C<gsl_sf_hyperg_U_int_e10_e>
2232 =item C<gsl_sf_hyperg_U_e>
2234 =item C<gsl_sf_hyperg_U >
2236 =item C<gsl_sf_hyperg_U_e10_e>
2238 =item C<gsl_sf_hyperg_2F1_e>
2240 =item C<gsl_sf_hyperg_2F1 >
2242 =item C<gsl_sf_hyperg_2F1_conj_e>
2244 =item C<gsl_sf_hyperg_2F1_conj>
2246 =item C<gsl_sf_hyperg_2F1_renorm_e >
2248 =item C<gsl_sf_hyperg_2F1_renorm>
2250 =item C<gsl_sf_hyperg_2F1_conj_renorm_e>
2252 =item C<gsl_sf_hyperg_2F1_conj_renorm >
2254 =item C<gsl_sf_hyperg_2F0_e>
2256 =item C<gsl_sf_hyperg_2F0>
2258 =item C<gsl_sf_laguerre_1_e >
2260 =item C<gsl_sf_laguerre_2_e>
2262 =item C<gsl_sf_laguerre_3_e>
2264 =item C<gsl_sf_laguerre_1 >
2266 =item C<gsl_sf_laguerre_2>
2268 =item C<gsl_sf_laguerre_3>
2270 =item C<gsl_sf_laguerre_n_e >
2272 =item C<gsl_sf_laguerre_n>
2274 =item C<gsl_sf_lambert_W0_e>
2276 =item C<gsl_sf_lambert_W0 >
2278 =item C<gsl_sf_lambert_Wm1_e>
2280 =item C<gsl_sf_lambert_Wm1>
2282 =item C<gsl_sf_conicalP_half_e >
2284 =item C<gsl_sf_conicalP_half>
2286 =item C<gsl_sf_conicalP_mhalf_e>
2288 =item C<gsl_sf_conicalP_mhalf >
2290 =item C<gsl_sf_conicalP_0_e>
2292 =item C<gsl_sf_conicalP_0>
2294 =item C<gsl_sf_conicalP_1_e >
2296 =item C<gsl_sf_conicalP_1>
2298 =item C<gsl_sf_conicalP_sph_reg_e>
2300 =item C<gsl_sf_conicalP_sph_reg >
2302 =item C<gsl_sf_conicalP_cyl_reg_e>
2304 =item C<gsl_sf_conicalP_cyl_reg>
2306 =item C<gsl_sf_legendre_H3d_0_e >
2308 =item C<gsl_sf_legendre_H3d_0>
2310 =item C<gsl_sf_legendre_H3d_1_e>
2312 =item C<gsl_sf_legendre_H3d_1 >
2314 =item C<gsl_sf_legendre_H3d_e>
2316 =item C<gsl_sf_legendre_H3d>
2318 =item C<gsl_sf_legendre_H3d_array >
2320 =item C<gsl_sf_log_e>
2322 =item C<gsl_sf_log>
2324 =item C<gsl_sf_log_abs_e >
2326 =item C<gsl_sf_log_abs>
2328 =item C<gsl_sf_complex_log_e>
2330 =item C<gsl_sf_log_1plusx_e >
2332 =item C<gsl_sf_log_1plusx>
2334 =item C<gsl_sf_log_1plusx_mx_e>
2336 =item C<gsl_sf_log_1plusx_mx >
2338 =item C<gsl_sf_mathieu_a_array>
2340 =item C<gsl_sf_mathieu_b_array>
2342 =item C<gsl_sf_mathieu_a >
2344 =item C<gsl_sf_mathieu_b>
2346 =item C<gsl_sf_mathieu_a_coeff>
2348 =item C<gsl_sf_mathieu_b_coeff >
2350 =item C<gsl_sf_mathieu_alloc>
2352 =item C<gsl_sf_mathieu_free>
2354 =item C<gsl_sf_mathieu_ce >
2356 =item C<gsl_sf_mathieu_se>
2358 =item C<gsl_sf_mathieu_ce_array>
2360 =item C<gsl_sf_mathieu_se_array >
2362 =item C<gsl_sf_mathieu_Mc>
2364 =item C<gsl_sf_mathieu_Ms>
2366 =item C<gsl_sf_mathieu_Mc_array >
2368 =item C<gsl_sf_mathieu_Ms_array>
2370 =item C<gsl_sf_pow_int_e>
2372 =item C<gsl_sf_pow_int >
2374 =item C<gsl_sf_psi_int_e>
2376 =item C<gsl_sf_psi_int>
2378 =item C<gsl_sf_psi_e >
2380 =item C<gsl_sf_psi>
2382 =item C<gsl_sf_psi_1piy_e>
2384 =item C<gsl_sf_psi_1piy >
2386 =item C<gsl_sf_complex_psi_e gsl_sf_psi_1_int_e>
2388 =item C<gsl_sf_psi_1_int >
2390 =item C<gsl_sf_psi_1_e >
2392 =item C<gsl_sf_psi_1>
2394 =item C<gsl_sf_psi_n_e >
2396 =item C<gsl_sf_psi_n>
2398 =item C<gsl_sf_result_smash_e>
2400 =item C<gsl_sf_synchrotron_1_e >
2402 =item C<gsl_sf_synchrotron_1>
2404 =item C<gsl_sf_synchrotron_2_e>
2406 =item C<gsl_sf_synchrotron_2 >
2408 =item C<gsl_sf_transport_2_e>
2410 =item C<gsl_sf_transport_2>
2412 =item C<gsl_sf_transport_3_e >
2414 =item C<gsl_sf_transport_3>
2416 =item C<gsl_sf_transport_4_e>
2418 =item C<gsl_sf_transport_4 >
2420 =item C<gsl_sf_transport_5_e>
2422 =item C<gsl_sf_transport_5>
2424 =item C<gsl_sf_sin_e >
2426 =item C<gsl_sf_sin>
2428 =item C<gsl_sf_cos_e>
2430 =item C<gsl_sf_cos >
2432 =item C<gsl_sf_hypot_e>
2434 =item C<gsl_sf_hypot>
2436 =item C<gsl_sf_complex_sin_e >
2438 =item C<gsl_sf_complex_cos_e>
2440 =item C<gsl_sf_complex_logsin_e>
2442 =item C<gsl_sf_sinc_e >
2444 =item C<gsl_sf_sinc>
2446 =item C<gsl_sf_lnsinh_e>
2448 =item C<gsl_sf_lnsinh >
2450 =item C<gsl_sf_lncosh_e>
2452 =item C<gsl_sf_lncosh>
2454 =item C<gsl_sf_polar_to_rect >
2456 =item C<gsl_sf_rect_to_polar>
2458 =item C<gsl_sf_sin_err_e>
2460 =item C<gsl_sf_cos_err_e >
2462 =item C<gsl_sf_angle_restrict_symm_e>
2464 =item C<gsl_sf_angle_restrict_symm>
2466 =item C<gsl_sf_angle_restrict_pos_e >
2468 =item C<gsl_sf_angle_restrict_pos>
2470 =item C<gsl_sf_angle_restrict_symm_err_e>
2472 =item C<gsl_sf_angle_restrict_pos_err_e >
2474 =item C<gsl_sf_atanint_e>
2476 =item C<gsl_sf_atanint>
2478 =item C<gsl_sf_zeta_int_e >
2480 =item C<gsl_sf_zeta_int>
2482 =item C<gsl_sf_zeta_e gsl_sf_zeta >
2484 =item C<gsl_sf_zetam1_e>
2486 =item C<gsl_sf_zetam1>
2488 =item C<gsl_sf_zetam1_int_e >
2490 =item C<gsl_sf_zetam1_int>
2492 =item C<gsl_sf_hzeta_e>
2494 =item C<gsl_sf_hzeta >
2496 =item C<gsl_sf_eta_int_e>
2498 =item C<gsl_sf_eta_int>
2500 =item C<gsl_sf_eta_e>
2502 =item C<gsl_sf_eta >
2504 =back
2506 You can import the functions that you want to use by giving a space separated
2507 list to Math::GSL::SF when you use the package. You can also write
2508 use Math::GSL::SF qw/:all/
2509 to use all avaible functions of the module. Note that
2510 the tag names begin with a colon. Other tags are also available, here is a
2511 complete list of all tags for this module :
2513 =over
2515 =item C<airy>
2517 =item C<bessel>
2519 =item C<clausen>
2521 =item C<hydrogenic>
2523 =item C<coulumb>
2525 =item C<coupling>
2527 =item C<dawson>
2529 =item C<debye>
2531 =item C<dilog>
2533 =item C<factorial>
2535 =item C<misc>
2537 =item C<elliptic>
2539 =item C<error>
2541 =item C<hypergeometric>
2543 =item C<laguerre>
2545 =item C<legendre>
2547 =item C<gamma>
2549 =item C<transport>
2551 =item C<trig>
2553 =item C<zeta>
2555 =item C<eta>
2557 =item C<vars>
2559 =back
2561 For more informations on the functions, we refer you to the GSL offcial
2562 documentation: L<http://www.gnu.org/software/gsl/manual/html_node/>
2564 Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/name_of_the_function_you_want
2566 =head1 EXAMPLES
2568 This example computes the dilogarithm of 1/10 :
2570 use Math::GSL::SF qw/dilog/;
2571 my $x = gsl_sf_dilog(0.1);
2572 print "gsl_sf_dilog(0.1) = $x\n";
2574 An example using Math::GSL::SF and gnuplot is in the B<examples/sf> folder of the source code.
2576 =head1 AUTHORS
2578 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
2580 =head1 COPYRIGHT AND LICENSE
2582 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
2584 This program is free software; you can redistribute it and/or modify it
2585 under the same terms as Perl itself.
2587 =cut