3 #include
"gsl/gsl_mode.h"
4 #include
"gsl/gsl_sf.h"
5 #include
"gsl/gsl_sf_airy.h"
6 #include
"gsl/gsl_sf_bessel.h"
7 #include
"gsl/gsl_sf_clausen.h"
8 #include
"gsl/gsl_sf_coulomb.h"
9 #include
"gsl/gsl_sf_coupling.h"
10 #include
"gsl/gsl_sf_dawson.h"
11 #include
"gsl/gsl_sf_debye.h"
12 #include
"gsl/gsl_sf_dilog.h"
13 #include
"gsl/gsl_sf_elementary.h"
14 #include
"gsl/gsl_sf_ellint.h"
15 #include
"gsl/gsl_sf_elljac.h"
16 #include
"gsl/gsl_sf_erf.h"
17 #include
"gsl/gsl_sf_exp.h"
18 #include
"gsl/gsl_sf_expint.h"
19 #include
"gsl/gsl_sf_fermi_dirac.h"
20 #include
"gsl/gsl_sf_gamma.h"
21 #include
"gsl/gsl_sf_gegenbauer.h"
22 #include
"gsl/gsl_sf_hyperg.h"
23 #include
"gsl/gsl_sf_laguerre.h"
24 #include
"gsl/gsl_sf_lambert.h"
25 #include
"gsl/gsl_sf_legendre.h"
26 #include
"gsl/gsl_sf_log.h"
27 #include
"gsl/gsl_sf_mathieu.h"
28 #include
"gsl/gsl_sf_pow_int.h"
29 #include
"gsl/gsl_sf_psi.h"
30 #include
"gsl/gsl_sf_result.h"
31 #include
"gsl/gsl_sf_synchrotron.h"
32 #include
"gsl/gsl_sf_transport.h"
33 #include
"gsl/gsl_sf_trig.h"
34 #include
"gsl/gsl_sf_zeta.h"
36 //%import
"gsl/gsl_types.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"
80 gsl_sf_airy_Ai_scaled_e
82 gsl_sf_airy_Bi_scaled_e
84 gsl_sf_airy_Ai_deriv_e
86 gsl_sf_airy_Bi_deriv_e
88 gsl_sf_airy_Ai_deriv_scaled_e
89 gsl_sf_airy_Ai_deriv_scaled
90 gsl_sf_airy_Bi_deriv_scaled_e
91 gsl_sf_airy_Bi_deriv_scaled
96 gsl_sf_airy_zero_Ai_deriv_e
97 gsl_sf_airy_zero_Ai_deriv
98 gsl_sf_airy_zero_Bi_deriv_e
99 gsl_sf_airy_zero_Bi_deriv
108 gsl_sf_bessel_Jn_array
115 gsl_sf_bessel_Yn_array
122 gsl_sf_bessel_In_array
123 gsl_sf_bessel_I0_scaled_e
124 gsl_sf_bessel_I0_scaled
125 gsl_sf_bessel_I1_scaled_e
126 gsl_sf_bessel_I1_scaled
127 gsl_sf_bessel_In_scaled_e
128 gsl_sf_bessel_In_scaled
129 gsl_sf_bessel_In_scaled_array
136 gsl_sf_bessel_Kn_array
137 gsl_sf_bessel_K0_scaled_e
138 gsl_sf_bessel_K0_scaled
139 gsl_sf_bessel_K1_scaled_e
140 gsl_sf_bessel_K1_scaled
141 gsl_sf_bessel_Kn_scaled_e
142 gsl_sf_bessel_Kn_scaled
143 gsl_sf_bessel_Kn_scaled_array
152 gsl_sf_bessel_jl_array
153 gsl_sf_bessel_jl_steed_array
162 gsl_sf_bessel_yl_array
163 gsl_sf_bessel_i0_scaled_e
164 gsl_sf_bessel_i0_scaled
165 gsl_sf_bessel_i1_scaled_e
166 gsl_sf_bessel_i1_scaled
167 gsl_sf_bessel_i2_scaled_e
168 gsl_sf_bessel_i2_scaled
169 gsl_sf_bessel_il_scaled_e
170 gsl_sf_bessel_il_scaled
171 gsl_sf_bessel_il_scaled_array
172 gsl_sf_bessel_k0_scaled_e
173 gsl_sf_bessel_k0_scaled
174 gsl_sf_bessel_k1_scaled_e
175 gsl_sf_bessel_k1_scaled
176 gsl_sf_bessel_k2_scaled_e
177 gsl_sf_bessel_k2_scaled
178 gsl_sf_bessel_kl_scaled_e
179 gsl_sf_bessel_kl_scaled
180 gsl_sf_bessel_kl_scaled_array
185 gsl_sf_bessel_sequence_Jnu_e
186 gsl_sf_bessel_Inu_scaled_e
187 gsl_sf_bessel_Inu_scaled
190 gsl_sf_bessel_Knu_scaled_e
191 gsl_sf_bessel_Knu_scaled
194 gsl_sf_bessel_lnKnu_e
196 gsl_sf_bessel_zero_J0_e
197 gsl_sf_bessel_zero_J0
198 gsl_sf_bessel_zero_J1_e
199 gsl_sf_bessel_zero_J1
200 gsl_sf_bessel_zero_Jnu_e
201 gsl_sf_bessel_zero_Jnu
203 @EXPORT_clausen
= qw
/
207 @EXPORT_hydrogenic
= qw
/
208 gsl_sf_hydrogenicR_1_e
213 @EXPORT_coulumb
= qw
/
214 gsl_sf_coulomb_wave_FG_e
215 gsl_sf_coulomb_wave_F_array
216 gsl_sf_coulomb_wave_FG_array
217 gsl_sf_coulomb_wave_FGp_array
218 gsl_sf_coulomb_wave_sphF_array
220 gsl_sf_coulomb_CL_array
222 @EXPORT_coupling
= qw
/
227 gsl_sf_coupling_RacahW_e
228 gsl_sf_coupling_RacahW
231 gsl_sf_coupling_6j_INCORRECT_e
232 gsl_sf_coupling_6j_INCORRECT
255 gsl_sf_complex_dilog_xy_e
256 gsl_sf_complex_dilog_e
260 gsl_sf_complex_spence_xy_e
263 gsl_sf_multiply_err_e
265 @EXPORT_elliptic
= qw
/
266 gsl_sf_ellint_Kcomp_e
268 gsl_sf_ellint_Ecomp_e
270 gsl_sf_ellint_Pcomp_e
272 gsl_sf_ellint_Dcomp_e
306 push @EXPORT_misc
, qw
/
312 gsl_sf_exp_mult_e10_e
323 gsl_sf_exp_mult_err_e
324 gsl_sf_exp_mult_err_e10_e
331 gsl_sf_expint_E1_scaled_e
332 gsl_sf_expint_E1_scaled
333 gsl_sf_expint_E2_scaled_e
334 gsl_sf_expint_E2_scaled
335 gsl_sf_expint_En_scaled_e
336 gsl_sf_expint_En_scaled
339 gsl_sf_expint_Ei_scaled_e
340 gsl_sf_expint_Ei_scaled
352 @EXPORT_fermi_dirac
= qw
/
353 gsl_sf_fermi_dirac_m1_e
354 gsl_sf_fermi_dirac_m1
355 gsl_sf_fermi_dirac_0_e
357 gsl_sf_fermi_dirac_1_e
359 gsl_sf_fermi_dirac_2_e
361 gsl_sf_fermi_dirac_int_e
362 gsl_sf_fermi_dirac_int
363 gsl_sf_fermi_dirac_mhalf_e
364 gsl_sf_fermi_dirac_mhalf
365 gsl_sf_fermi_dirac_half_e
366 gsl_sf_fermi_dirac_half
367 gsl_sf_fermi_dirac_3half_e
368 gsl_sf_fermi_dirac_3half
369 gsl_sf_fermi_dirac_inc_0_e
370 gsl_sf_fermi_dirac_inc_0
372 @EXPORT_legendre
= qw
/
375 gsl_sf_legendre_Pl_array
376 gsl_sf_legendre_Pl_deriv_array
389 gsl_sf_legendre_Plm_e
391 gsl_sf_legendre_Plm_array
392 gsl_sf_legendre_Plm_deriv_array
393 gsl_sf_legendre_sphPlm_e
394 gsl_sf_legendre_sphPlm
395 gsl_sf_legendre_sphPlm_array
396 gsl_sf_legendre_sphPlm_deriv_array
397 gsl_sf_legendre_array_size
398 gsl_sf_legendre_H3d_0_e
399 gsl_sf_legendre_H3d_0
400 gsl_sf_legendre_H3d_1_e
401 gsl_sf_legendre_H3d_1
402 gsl_sf_legendre_H3d_e
404 gsl_sf_legendre_H3d_array
416 gsl_sf_lngamma_complex_e
424 @EXPORT_factorial
= qw
/
431 gsl_sf_lndoublefact_e
434 @EXPORT_hypergeometric
= qw
/
437 gsl_sf_hyperg_1F1_int_e
438 gsl_sf_hyperg_1F1_int
441 gsl_sf_hyperg_U_int_e
443 gsl_sf_hyperg_U_int_e10_e
446 gsl_sf_hyperg_U_e10_e
449 gsl_sf_hyperg_2F1_conj_e
450 gsl_sf_hyperg_2F1_conj
451 gsl_sf_hyperg_2F1_renorm_e
452 gsl_sf_hyperg_2F1_renorm
453 gsl_sf_hyperg_2F1_conj_renorm_e
454 gsl_sf_hyperg_2F1_conj_renorm
458 @EXPORT_laguerre
= qw
/
468 push @EXPORT_misc
, qw
/
497 gsl_sf_gegenpoly_array
502 gsl_sf_conicalP_half_e
504 gsl_sf_conicalP_mhalf_e
505 gsl_sf_conicalP_mhalf
510 gsl_sf_conicalP_sph_reg_e
511 gsl_sf_conicalP_sph_reg
512 gsl_sf_conicalP_cyl_reg_e
513 gsl_sf_conicalP_cyl_reg
521 gsl_sf_log_1plusx_mx_e
538 gsl_sf_result_smash_e
539 gsl_sf_synchrotron_1_e
541 gsl_sf_synchrotron_2_e
544 @EXPORT_mathieu
= qw
/
545 gsl_sf_mathieu_a_array
546 gsl_sf_mathieu_b_array
549 gsl_sf_mathieu_a_coeff
550 gsl_sf_mathieu_b_coeff
555 gsl_sf_mathieu_ce_array
556 gsl_sf_mathieu_se_array
559 gsl_sf_mathieu_Mc_array
560 gsl_sf_mathieu_Ms_array
562 @EXPORT_transport
= qw
/
583 gsl_sf_complex_logsin_e
594 gsl_sf_angle_restrict_symm_e
595 gsl_sf_angle_restrict_symm
596 gsl_sf_angle_restrict_pos_e
597 gsl_sf_angle_restrict_pos
598 gsl_sf_angle_restrict_symm_err_e
599 gsl_sf_angle_restrict_pos_err_e
624 GSL_SF_DOUBLEFACT_NMAX
629 @EXPORT_airy
, @EXPORT_bessel
, @EXPORT_clausen
, @EXPORT_hydrogenic
,
630 @EXPORT_coulumb
, @EXPORT_coupling
, @EXPORT_dawson
, @EXPORT_debye
,
631 @EXPORT_dilog
, @EXPORT_misc
, @EXPORT_elliptic
, @EXPORT_error
, @EXPORT_legendre
,
632 @EXPORT_gamma
, @EXPORT_transport
, @EXPORT_trig
, @EXPORT_zeta
, @EXPORT_eta
,
637 all
=> [ @EXPORT_OK
],
638 airy
=> [ @EXPORT_airy
],
639 bessel
=> [ @EXPORT_bessel
],
640 clausen
=> [ @EXPORT_clausen
],
641 coulumb
=> [ @EXPORT_coulumb
],
642 coupling
=> [ @EXPORT_coupling
],
643 dawson
=> [ @EXPORT_dawson
],
644 debye
=> [ @EXPORT_debye
],
645 dilog
=> [ @EXPORT_dilog
],
646 eta
=> [ @EXPORT_eta
],
647 elliptic
=> [ @EXPORT_elliptic
],
648 error
=> [ @EXPORT_error
],
649 factorial
=> [ @EXPORT_factorial
],
650 gamma
=> [ @EXPORT_gamma
],
651 hydrogenic
=> [ @EXPORT_hydrogenic
],
652 hypergeometric
=> [ @EXPORT_hypergeometric
],
653 laguerre
=> [ @EXPORT_laguerre
],
654 legendre
=> [ @EXPORT_legendre
],
655 mathieu
=> [ @EXPORT_mathieu
],
656 misc
=> [ @EXPORT_misc
],
657 transport
=> [ @EXPORT_transport
],
658 trig
=> [ @EXPORT_trig
],
659 vars
=> [ @EXPORT_vars
],
660 zeta
=> [ @EXPORT_zeta
],
667 Math
::GSL
::SF
- Special Functions
671 use Math
::GSL
::SF qw
/:all
/;
675 This module contains a data structure named gsl_sf_result. To create a new one use
676 $r
= Math
::GSL
::SF
::gsl_sf_result_struct-
>new
;
677 You can then access the elements of the structure in this way
:
682 Here is a list of all included functions
:
686 =item C
<gsl_sf_airy_Ai_e
($x
, $mode
)>
688 =item C
<gsl_sf_airy_Ai
($x
, $mode
, $result
)>
690 - These routines compute the Airy function Ai
($x
) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE
, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
696 =item C
<gsl_sf_airy_Bi_e
($x
, $mode
, $result
)>
698 =item C
<gsl_sf_airy_Bi
($x
, $mode
)>
700 - These routines compute the Airy function Bi
($x
) with an accuracy specified by $mode. $mode should be $GSL_PREC_DOUBLE
, $GSL_PREC_SINGLE or $GSL_PREC_APPROX. $result is a gsl_sf_result structure.
706 =item C
<gsl_sf_airy_Ai_scaled_e
($x
, $mode
, $result
)>
708 =item C
<gsl_sf_airy_Ai_scaled
($x
, $mode
)>
710 - These routines compute a scaled version of the Airy function S_A
($x
) Ai
($x
). For $x
>0 the scaling factor S_A
($x
) is \exp
(+(2/3) $x
**(3/2)), and is
1 for $x
<0.
716 =item C
<gsl_sf_airy_Bi_scaled_e
($x
, $mode
, $result
)>
718 =item C
<gsl_sf_airy_Bi_scaled
($x
, $mode
)>
720 - These routines compute a scaled version of the Airy function S_B
($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.
726 =item C
<gsl_sf_airy_Ai_deriv_e
>
728 =item C
<gsl_sf_airy_Ai_deriv
>
730 =item C
<gsl_sf_airy_Bi_deriv_e
>
732 =item C
<gsl_sf_airy_Bi_deriv
>
734 =item C
<gsl_sf_airy_Ai_deriv_scaled_e
>
736 =item C
<gsl_sf_airy_Ai_deriv_scaled
>
738 =item C
<gsl_sf_airy_Bi_deriv_scaled_e
>
740 =item C
<gsl_sf_airy_Bi_deriv_scaled
>
742 =item C
<gsl_sf_airy_zero_Ai_e
>
744 =item C
<gsl_sf_airy_zero_Ai
>
746 =item C
<gsl_sf_airy_zero_Bi_e
>
748 =item C
<gsl_sf_airy_zero_Bi
>
750 =item C
<gsl_sf_airy_zero_Ai_deriv_e
>
752 =item C
<gsl_sf_airy_zero_Ai_deriv
>
754 =item C
<gsl_sf_airy_zero_Bi_deriv_e
>
756 =item C
<gsl_sf_airy_zero_Bi_deriv
>
758 =item C
<gsl_sf_bessel_J0_e
>
760 =item C
<gsl_sf_bessel_J0
>
762 =item C
<gsl_sf_bessel_J1_e
>
764 =item C
<gsl_sf_bessel_J1
>
766 =item C
<gsl_sf_bessel_Jn_e
>
768 =item C
<gsl_sf_bessel_Jn
>
770 =item C
<gsl_sf_bessel_Jn_array
>
772 =item C
<gsl_sf_bessel_Y0_e
>
774 =item C
<gsl_sf_bessel_Y0
>
776 =item C
<gsl_sf_bessel_Y1_e
>
778 =item C
<gsl_sf_bessel_Y1
>
780 =item C
<gsl_sf_bessel_Yn_e
>
782 =item C
<gsl_sf_bessel_Yn
>
784 =item C
<gsl_sf_bessel_Yn_array
>
786 =item C
<gsl_sf_bessel_I0_e
>
788 =item C
<gsl_sf_bessel_I0
>
790 =item C
<gsl_sf_bessel_I1_e
>
792 =item C
<gsl_sf_bessel_I1
>
794 =item C
<gsl_sf_bessel_In_e
>
796 =item C
<gsl_sf_bessel_In
>
798 =item C
<gsl_sf_bessel_In_array
>
800 =item C
<gsl_sf_bessel_I0_scaled_e
>
802 =item C
<gsl_sf_bessel_I0_scaled
>
804 =item C
<gsl_sf_bessel_I1_scaled_e
>
806 =item C
<gsl_sf_bessel_I1_scaled
>
808 =item C
<gsl_sf_bessel_In_scaled_e
>
810 =item C
<gsl_sf_bessel_In_scaled
>
812 =item C
<gsl_sf_bessel_In_scaled_array
>
814 =item C
<gsl_sf_bessel_K0_e
>
816 =item C
<gsl_sf_bessel_K0
>
818 =item C
<gsl_sf_bessel_K1_e
>
820 =item C
<gsl_sf_bessel_K1
>
822 =item C
<gsl_sf_bessel_Kn_e
>
824 =item C
<gsl_sf_bessel_Kn
>
826 =item C
<gsl_sf_bessel_Kn_array
>
828 =item C
<gsl_sf_bessel_K0_scaled_e
>
830 =item C
<gsl_sf_bessel_K0_scaled
>
832 =item C
<gsl_sf_bessel_K1_scaled_e
>
834 =item C
<gsl_sf_bessel_K1_scaled
>
836 =item C
<gsl_sf_bessel_Kn_scaled_e
>
838 =item C
<gsl_sf_bessel_Kn_scaled
>
840 =item C
<gsl_sf_bessel_Kn_scaled_array
>
842 =item C
<gsl_sf_bessel_j0_e
>
844 =item C
<gsl_sf_bessel_j0
>
846 =item C
<gsl_sf_bessel_j1_e
>
848 =item C
<gsl_sf_bessel_j1
>
850 =item C
<gsl_sf_bessel_j2_e
>
852 =item C
<gsl_sf_bessel_j2
>
854 =item C
<gsl_sf_bessel_jl_e
>
856 =item C
<gsl_sf_bessel_jl
>
858 =item C
<gsl_sf_bessel_jl_array
>
860 =item C
<gsl_sf_bessel_jl_steed_array
>
862 =item C
<gsl_sf_bessel_y0_e
>
864 =item C
<gsl_sf_bessel_y0
>
866 =item C
<gsl_sf_bessel_y1_e
>
868 =item C
<gsl_sf_bessel_y1
>
870 =item C
<gsl_sf_bessel_y2_e
>
872 =item C
<gsl_sf_bessel_y2
>
874 =item C
<gsl_sf_bessel_yl_e
>
876 =item C
<gsl_sf_bessel_yl
>
878 =item C
<gsl_sf_bessel_yl_array
>
880 =item C
<gsl_sf_bessel_i0_scaled_e
>
882 =item C
<gsl_sf_bessel_i0_scaled
>
884 =item C
<gsl_sf_bessel_i1_scaled_e
>
886 =item C
<gsl_sf_bessel_i1_scaled
>
888 =item C
<gsl_sf_bessel_i2_scaled_e
>
890 =item C
<gsl_sf_bessel_i2_scaled
>
892 =item C
<gsl_sf_bessel_il_scaled_e
>
894 =item C
<gsl_sf_bessel_il_scaled
>
896 =item C
<gsl_sf_bessel_il_scaled_array
>
898 =item C
<gsl_sf_bessel_k0_scaled_e
>
900 =item C
<gsl_sf_bessel_k0_scaled
>
902 =item C
<gsl_sf_bessel_k1_scaled_e
>
904 =item C
<gsl_sf_bessel_k1_scaled
>
906 =item C
<gsl_sf_bessel_k2_scaled_e
>
908 =item C
<gsl_sf_bessel_k2_scaled
>
910 =item C
<gsl_sf_bessel_kl_scaled_e
>
912 =item C
<gsl_sf_bessel_kl_scaled
>
914 =item C
<gsl_sf_bessel_kl_scaled_array
>
916 =item C
<gsl_sf_bessel_Jnu_e
>
918 =item C
<gsl_sf_bessel_Jnu
>
920 =item C
<gsl_sf_bessel_Ynu_e
>
922 =item C
<gsl_sf_bessel_Ynu
>
924 =item C
<gsl_sf_bessel_sequence_Jnu_e
>
926 =item C
<gsl_sf_bessel_Inu_scaled_e
>
928 =item C
<gsl_sf_bessel_Inu_scaled
>
930 =item C
<gsl_sf_bessel_Inu_e
>
932 =item C
<gsl_sf_bessel_Inu
>
934 =item C
<gsl_sf_bessel_Knu_scaled_e
>
936 =item C
<gsl_sf_bessel_Knu_scaled
>
938 =item C
<gsl_sf_bessel_Knu_e
>
940 =item C
<gsl_sf_bessel_Knu
>
942 =item C
<gsl_sf_bessel_lnKnu_e
>
944 =item C
<gsl_sf_bessel_lnKnu
>
946 =item C
<gsl_sf_bessel_zero_J0_e
>
948 =item C
<gsl_sf_bessel_zero_J0
>
950 =item C
<gsl_sf_bessel_zero_J1_e
>
952 =item C
<gsl_sf_bessel_zero_J1
>
954 =item C
<gsl_sf_bessel_zero_Jnu_e
>
956 =item C
<gsl_sf_bessel_zero_Jnu
>
958 =item C
<gsl_sf_clausen_e
>
960 =item C
<gsl_sf_clausen
>
962 =item C
<gsl_sf_hydrogenicR_1_e
>
964 =item C
<gsl_sf_hydrogenicR_1
>
966 =item C
<gsl_sf_hydrogenicR_e
>
968 =item C
<gsl_sf_hydrogenicR
>
970 =item C
<gsl_sf_coulomb_wave_FG_e
>
972 =item C
<gsl_sf_coulomb_wave_F_array
>
974 =item C
<gsl_sf_coulomb_wave_FG_array
>
976 =item C
<gsl_sf_coulomb_wave_FGp_array
>
978 =item C
<gsl_sf_coulomb_wave_sphF_array
>
980 =item C
<gsl_sf_coulomb_CL_e
>
982 =item C
<gsl_sf_coulomb_CL_array
>
984 =item C
<gsl_sf_coupling_3j_e
>
986 =item C
<gsl_sf_coupling_3j
>
988 =item C
<gsl_sf_coupling_6j_e
>
990 =item C
<gsl_sf_coupling_6j
>
992 =item C
<gsl_sf_coupling_RacahW_e
>
994 =item C
<gsl_sf_coupling_RacahW
>
996 =item C
<gsl_sf_coupling_9j_e
>
998 =item C
<gsl_sf_coupling_9j
>
1000 =item C
<gsl_sf_coupling_6j_INCORRECT_e
>
1002 =item C
<gsl_sf_coupling_6j_INCORRECT
>
1004 =item C
<gsl_sf_dawson_e
, gsl_sf_dawson
>
1006 =item C
<gsl_sf_debye_1_e
>
1008 =item C
<gsl_sf_debye_1
>
1010 =item C
<gsl_sf_debye_2_e
>
1012 =item C
<gsl_sf_debye_2
>
1014 =item C
<gsl_sf_debye_3_e
>
1016 =item C
<gsl_sf_debye_3
>
1018 =item C
<gsl_sf_debye_4_e
>
1020 =item C
<gsl_sf_debye_4
>
1022 =item C
<gsl_sf_debye_5_e
>
1024 =item C
<gsl_sf_debye_5
>
1026 =item C
<gsl_sf_debye_6_e
>
1028 =item C
<gsl_sf_debye_6
>
1030 =item C
<gsl_sf_dilog_e
>
1032 =item C
<gsl_sf_dilog
>
1034 =item C
<gsl_sf_complex_dilog_xy_e
>
1036 =item C
<gsl_sf_complex_dilog_e
>
1038 =item C
<gsl_sf_complex_spence_xy_e
>
1040 =item C
<gsl_sf_multiply_e
>
1042 =item C
<gsl_sf_multiply
>
1044 =item C
<gsl_sf_multiply_err_e
>
1046 =item C
<gsl_sf_ellint_Kcomp_e gsl_sf_ellint_Kcomp
>
1048 =item C
<gsl_sf_ellint_Ecomp_e
>
1050 =item C
<gsl_sf_ellint_Ecomp
>
1052 =item C
<gsl_sf_ellint_Pcomp_e
>
1054 =item C
<gsl_sf_ellint_Pcomp
>
1056 =item C
<gsl_sf_ellint_Dcomp_e
>
1058 =item C
<gsl_sf_ellint_Dcomp
>
1060 =item C
<gsl_sf_ellint_F_e
>
1062 =item C
<gsl_sf_ellint_F
>
1064 =item C
<gsl_sf_ellint_E_e
>
1066 =item C
<gsl_sf_ellint_E
>
1068 =item C
<gsl_sf_ellint_P_e
>
1070 =item C
<gsl_sf_ellint_P
>
1072 =item C
<gsl_sf_ellint_D_e
>
1074 =item C
<gsl_sf_ellint_D
>
1076 =item C
<gsl_sf_ellint_RC_e
>
1078 =item C
<gsl_sf_ellint_RC
>
1080 =item C
<gsl_sf_ellint_RD_e
>
1082 =item C
<gsl_sf_ellint_RD
>
1084 =item C
<gsl_sf_ellint_RF_e
>
1086 =item C
<gsl_sf_ellint_RF
>
1088 =item C
<gsl_sf_ellint_RJ_e
>
1090 =item C
<gsl_sf_ellint_RJ
>
1092 =item C
<gsl_sf_elljac_e
>
1094 =item C
<gsl_sf_erfc_e
>
1096 =item C
<gsl_sf_erfc
>
1098 =item C
<gsl_sf_log_erfc_e
>
1100 =item C
<gsl_sf_log_erfc
>
1102 =item C
<gsl_sf_erf_e
>
1106 =item C
<gsl_sf_erf_Z_e
>
1108 =item C
<gsl_sf_erf_Q_e
>
1110 =item C
<gsl_sf_erf_Z
>
1112 =item C
<gsl_sf_erf_Q
>
1114 =item C
<gsl_sf_hazard_e
>
1116 =item C
<gsl_sf_hazard
>
1118 =item C
<gsl_sf_exp_e
>
1122 =item C
<gsl_sf_exp_e10_e
>
1124 =item C
<gsl_sf_exp_mult_e
>
1126 =item C
<gsl_sf_exp_mult
>
1128 =item C
<gsl_sf_exp_mult_e10_e
>
1130 =item C
<gsl_sf_expm1_e
>
1132 =item C
<gsl_sf_expm1
>
1134 =item C
<gsl_sf_exprel_e
>
1136 =item C
<gsl_sf_exprel
>
1138 =item C
<gsl_sf_exprel_2_e
>
1140 =item C
<gsl_sf_exprel_2
>
1142 =item C
<gsl_sf_exprel_n_e
>
1144 =item C
<gsl_sf_exprel_n
>
1146 =item C
<gsl_sf_exp_err_e
>
1148 =item C
<gsl_sf_exp_err_e10_e
>
1150 =item C
<gsl_sf_exp_mult_err_e
>
1152 =item C
<gsl_sf_exp_mult_err_e10_e
>
1154 =item C
<gsl_sf_expint_E1_e
>
1156 =item C
<gsl_sf_expint_E1
>
1158 =item C
<gsl_sf_expint_E2_e
>
1160 =item C
<gsl_sf_expint_E2
>
1162 =item C
<gsl_sf_expint_En_e
>
1164 =item C
<gsl_sf_expint_En
>
1166 =item C
<gsl_sf_expint_E1_scaled_e
>
1168 =item C
<gsl_sf_expint_E1_scaled
>
1170 =item C
<gsl_sf_expint_E2_scaled_e
>
1172 =item C
<gsl_sf_expint_E2_scaled
>
1174 =item C
<gsl_sf_expint_En_scaled_e
>
1176 =item C
<gsl_sf_expint_En_scaled
>
1178 =item C
<gsl_sf_expint_Ei_e
>
1180 =item C
<gsl_sf_expint_Ei
>
1182 =item C
<gsl_sf_expint_Ei_scaled_e
>
1184 =item C
<gsl_sf_expint_Ei_scaled
>
1186 =item C
<gsl_sf_Shi_e
>
1190 =item C
<gsl_sf_Chi_e
>
1194 =item C
<gsl_sf_expint_3_e
>
1196 =item C
<gsl_sf_expint_3
>
1198 =item C
<gsl_sf_Si_e
>
1202 =item C
<gsl_sf_Ci_e
>
1206 =item C
<gsl_sf_fermi_dirac_m1_e
>
1208 =item C
<gsl_sf_fermi_dirac_m1
>
1210 =item C
<gsl_sf_fermi_dirac_0_e
>
1212 =item C
<gsl_sf_fermi_dirac_0
>
1214 =item C
<gsl_sf_fermi_dirac_1_e
>
1216 =item C
<gsl_sf_fermi_dirac_1
>
1218 =item C
<gsl_sf_fermi_dirac_2_e
>
1220 =item C
<gsl_sf_fermi_dirac_2
>
1222 =item C
<gsl_sf_fermi_dirac_int_e
>
1224 =item C
<gsl_sf_fermi_dirac_int
>
1226 =item C
<gsl_sf_fermi_dirac_mhalf_e
>
1228 =item C
<gsl_sf_fermi_dirac_mhalf
>
1230 =item C
<gsl_sf_fermi_dirac_half_e
>
1232 =item C
<gsl_sf_fermi_dirac_half
>
1234 =item C
<gsl_sf_fermi_dirac_3half_e
>
1236 =item C
<gsl_sf_fermi_dirac_3half
>
1238 =item C
<gsl_sf_fermi_dirac_inc_0_e
>
1240 =item C
<gsl_sf_fermi_dirac_inc_0
>
1242 =item C
<gsl_sf_legendre_Pl_e
>
1244 =item C
<gsl_sf_legendre_Pl
>
1246 =item C
<gsl_sf_legendre_Pl_array
>
1248 =item C
<gsl_sf_legendre_Pl_deriv_array
>
1250 =item C
<gsl_sf_legendre_P1_e
>
1252 =item C
<gsl_sf_legendre_P2_e
>
1254 =item C
<gsl_sf_legendre_P3_e
>
1256 =item C
<gsl_sf_legendre_P1
>
1258 =item C
<gsl_sf_legendre_P2
>
1260 =item C
<gsl_sf_legendre_P3
>
1262 =item C
<gsl_sf_legendre_Q0_e
>
1264 =item C
<gsl_sf_legendre_Q0
>
1266 =item C
<gsl_sf_legendre_Q1_e
>
1268 =item C
<gsl_sf_legendre_Q1
>
1270 =item C
<gsl_sf_legendre_Ql_e
>
1272 =item C
<gsl_sf_legendre_Ql
>
1274 =item C
<gsl_sf_legendre_Plm_e
>
1276 =item C
<gsl_sf_legendre_Plm
>
1278 =item C
<gsl_sf_legendre_Plm_array
>
1280 =item C
<gsl_sf_legendre_Plm_deriv_array
>
1282 =item C
<gsl_sf_legendre_sphPlm_e
>
1284 =item C
<gsl_sf_legendre_sphPlm
>
1286 =item C
<gsl_sf_legendre_sphPlm_array
>
1288 =item C
<gsl_sf_legendre_sphPlm_deriv_array
>
1290 =item C
<gsl_sf_legendre_array_size
>
1292 =item C
<gsl_sf_lngamma_e
>
1294 =item C
<gsl_sf_lngamma
>
1296 =item C
<gsl_sf_lngamma_sgn_e
>
1298 =item C
<gsl_sf_gamma_e
>
1300 =item C
<gsl_sf_gamma
>
1302 =item C
<gsl_sf_gammastar_e
>
1304 =item C
<gsl_sf_gammastar
>
1306 =item C
<gsl_sf_gammainv_e
>
1308 =item C
<gsl_sf_gammainv
>
1310 =item C
<gsl_sf_lngamma_complex_e
>
1312 =item C
<gsl_sf_gamma_inc_Q_e
>
1314 =item C
<gsl_sf_gamma_inc_Q
>
1316 =item C
<gsl_sf_gamma_inc_P_e
>
1318 =item C
<gsl_sf_gamma_inc_P
>
1320 =item C
<gsl_sf_gamma_inc_e
>
1322 =item C
<gsl_sf_gamma_inc
>
1324 =item C
<gsl_sf_taylorcoeff_e
>
1326 =item C
<gsl_sf_taylorcoeff
>
1328 =item C
<gsl_sf_fact_e
>
1330 =item C
<gsl_sf_fact
>
1332 =item C
<gsl_sf_doublefact_e
>
1334 =item C
<gsl_sf_doublefact
>
1336 =item C
<gsl_sf_lnfact_e
>
1338 =item C
<gsl_sf_lnfact
>
1340 =item C
<gsl_sf_lndoublefact_e
>
1342 =item C
<gsl_sf_lndoublefact
>
1344 =item C
<gsl_sf_lnchoose_e
>
1346 =item C
<gsl_sf_lnchoose
>
1348 =item C
<gsl_sf_choose_e
>
1350 =item C
<gsl_sf_choose
>
1352 =item C
<gsl_sf_lnpoch_e
>
1354 =item C
<gsl_sf_lnpoch
>
1356 =item C
<gsl_sf_lnpoch_sgn_e
>
1358 =item C
<gsl_sf_poch_e
>
1360 =item C
<gsl_sf_poch
>
1362 =item C
<gsl_sf_pochrel_e
>
1364 =item C
<gsl_sf_pochrel
>
1366 =item C
<gsl_sf_lnbeta_e
>
1368 =item C
<gsl_sf_lnbeta
>
1370 =item C
<gsl_sf_lnbeta_sgn_e
>
1372 =item C
<gsl_sf_beta_e
>
1374 =item C
<gsl_sf_beta
>
1376 =item C
<gsl_sf_beta_inc_e
>
1378 =item C
<gsl_sf_beta_inc
>
1380 =item C
<gsl_sf_gegenpoly_1_e
>
1382 =item C
<gsl_sf_gegenpoly_2_e
>
1384 =item C
<gsl_sf_gegenpoly_3_e
>
1386 =item C
<gsl_sf_gegenpoly_1
>
1388 =item C
<gsl_sf_gegenpoly_2
>
1390 =item C
<gsl_sf_gegenpoly_3
>
1392 =item C
<gsl_sf_gegenpoly_n_e
>
1394 =item C
<gsl_sf_gegenpoly_n
>
1396 =item C
<gsl_sf_gegenpoly_array
>
1398 =item C
<gsl_sf_hyperg_0F1_e
>
1400 =item C
<gsl_sf_hyperg_0F1
>
1402 =item C
<gsl_sf_hyperg_1F1_int_e
>
1404 =item C
<gsl_sf_hyperg_1F1_int
>
1406 =item C
<gsl_sf_hyperg_1F1_e
>
1408 =item C
<gsl_sf_hyperg_1F1
>
1410 =item C
<gsl_sf_hyperg_U_int_e
>
1412 =item C
<gsl_sf_hyperg_U_int
>
1414 =item C
<gsl_sf_hyperg_U_int_e10_e
>
1416 =item C
<gsl_sf_hyperg_U_e
>
1418 =item C
<gsl_sf_hyperg_U
>
1420 =item C
<gsl_sf_hyperg_U_e10_e
>
1422 =item C
<gsl_sf_hyperg_2F1_e
>
1424 =item C
<gsl_sf_hyperg_2F1
>
1426 =item C
<gsl_sf_hyperg_2F1_conj_e
>
1428 =item C
<gsl_sf_hyperg_2F1_conj
>
1430 =item C
<gsl_sf_hyperg_2F1_renorm_e
>
1432 =item C
<gsl_sf_hyperg_2F1_renorm
>
1434 =item C
<gsl_sf_hyperg_2F1_conj_renorm_e
>
1436 =item C
<gsl_sf_hyperg_2F1_conj_renorm
>
1438 =item C
<gsl_sf_hyperg_2F0_e
>
1440 =item C
<gsl_sf_hyperg_2F0
>
1442 =item C
<gsl_sf_laguerre_1_e
>
1444 =item C
<gsl_sf_laguerre_2_e
>
1446 =item C
<gsl_sf_laguerre_3_e
>
1448 =item C
<gsl_sf_laguerre_1
>
1450 =item C
<gsl_sf_laguerre_2
>
1452 =item C
<gsl_sf_laguerre_3
>
1454 =item C
<gsl_sf_laguerre_n_e
>
1456 =item C
<gsl_sf_laguerre_n
>
1458 =item C
<gsl_sf_lambert_W0_e
>
1460 =item C
<gsl_sf_lambert_W0
>
1462 =item C
<gsl_sf_lambert_Wm1_e
>
1464 =item C
<gsl_sf_lambert_Wm1
>
1466 =item C
<gsl_sf_conicalP_half_e
>
1468 =item C
<gsl_sf_conicalP_half
>
1470 =item C
<gsl_sf_conicalP_mhalf_e
>
1472 =item C
<gsl_sf_conicalP_mhalf
>
1474 =item C
<gsl_sf_conicalP_0_e
>
1476 =item C
<gsl_sf_conicalP_0
>
1478 =item C
<gsl_sf_conicalP_1_e
>
1480 =item C
<gsl_sf_conicalP_1
>
1482 =item C
<gsl_sf_conicalP_sph_reg_e
>
1484 =item C
<gsl_sf_conicalP_sph_reg
>
1486 =item C
<gsl_sf_conicalP_cyl_reg_e
>
1488 =item C
<gsl_sf_conicalP_cyl_reg
>
1490 =item C
<gsl_sf_legendre_H3d_0_e
>
1492 =item C
<gsl_sf_legendre_H3d_0
>
1494 =item C
<gsl_sf_legendre_H3d_1_e
>
1496 =item C
<gsl_sf_legendre_H3d_1
>
1498 =item C
<gsl_sf_legendre_H3d_e
>
1500 =item C
<gsl_sf_legendre_H3d
>
1502 =item C
<gsl_sf_legendre_H3d_array
>
1504 =item C
<gsl_sf_log_e
>
1508 =item C
<gsl_sf_log_abs_e
>
1510 =item C
<gsl_sf_log_abs
>
1512 =item C
<gsl_sf_complex_log_e
>
1514 =item C
<gsl_sf_log_1plusx_e
>
1516 =item C
<gsl_sf_log_1plusx
>
1518 =item C
<gsl_sf_log_1plusx_mx_e
>
1520 =item C
<gsl_sf_log_1plusx_mx
>
1522 =item C
<gsl_sf_mathieu_a_array
>
1524 =item C
<gsl_sf_mathieu_b_array
>
1526 =item C
<gsl_sf_mathieu_a
>
1528 =item C
<gsl_sf_mathieu_b
>
1530 =item C
<gsl_sf_mathieu_a_coeff
>
1532 =item C
<gsl_sf_mathieu_b_coeff
>
1534 =item C
<gsl_sf_mathieu_alloc
>
1536 =item C
<gsl_sf_mathieu_free
>
1538 =item C
<gsl_sf_mathieu_ce
>
1540 =item C
<gsl_sf_mathieu_se
>
1542 =item C
<gsl_sf_mathieu_ce_array
>
1544 =item C
<gsl_sf_mathieu_se_array
>
1546 =item C
<gsl_sf_mathieu_Mc
>
1548 =item C
<gsl_sf_mathieu_Ms
>
1550 =item C
<gsl_sf_mathieu_Mc_array
>
1552 =item C
<gsl_sf_mathieu_Ms_array
>
1554 =item C
<gsl_sf_pow_int_e
>
1556 =item C
<gsl_sf_pow_int
>
1558 =item C
<gsl_sf_psi_int_e
>
1560 =item C
<gsl_sf_psi_int
>
1562 =item C
<gsl_sf_psi_e
>
1566 =item C
<gsl_sf_psi_1piy_e
>
1568 =item C
<gsl_sf_psi_1piy
>
1570 =item C
<gsl_sf_complex_psi_e gsl_sf_psi_1_int_e
>
1572 =item C
<gsl_sf_psi_1_int
>
1574 =item C
<gsl_sf_psi_1_e
>
1576 =item C
<gsl_sf_psi_1
>
1578 =item C
<gsl_sf_psi_n_e
>
1580 =item C
<gsl_sf_psi_n
>
1582 =item C
<gsl_sf_result_smash_e
>
1584 =item C
<gsl_sf_synchrotron_1_e
>
1586 =item C
<gsl_sf_synchrotron_1
>
1588 =item C
<gsl_sf_synchrotron_2_e
>
1590 =item C
<gsl_sf_synchrotron_2
>
1592 =item C
<gsl_sf_transport_2_e
>
1594 =item C
<gsl_sf_transport_2
>
1596 =item C
<gsl_sf_transport_3_e
>
1598 =item C
<gsl_sf_transport_3
>
1600 =item C
<gsl_sf_transport_4_e
>
1602 =item C
<gsl_sf_transport_4
>
1604 =item C
<gsl_sf_transport_5_e
>
1606 =item C
<gsl_sf_transport_5
>
1608 =item C
<gsl_sf_sin_e
>
1612 =item C
<gsl_sf_cos_e
>
1614 =item C
<gsl_sf_cos
>
1616 =item C
<gsl_sf_hypot_e
>
1618 =item C
<gsl_sf_hypot
>
1620 =item C
<gsl_sf_complex_sin_e
>
1622 =item C
<gsl_sf_complex_cos_e
>
1624 =item C
<gsl_sf_complex_logsin_e
>
1626 =item C
<gsl_sf_sinc_e
>
1628 =item C
<gsl_sf_sinc
>
1630 =item C
<gsl_sf_lnsinh_e
>
1632 =item C
<gsl_sf_lnsinh
>
1634 =item C
<gsl_sf_lncosh_e
>
1636 =item C
<gsl_sf_lncosh
>
1638 =item C
<gsl_sf_polar_to_rect
>
1640 =item C
<gsl_sf_rect_to_polar
>
1642 =item C
<gsl_sf_sin_err_e
>
1644 =item C
<gsl_sf_cos_err_e
>
1646 =item C
<gsl_sf_angle_restrict_symm_e
>
1648 =item C
<gsl_sf_angle_restrict_symm
>
1650 =item C
<gsl_sf_angle_restrict_pos_e
>
1652 =item C
<gsl_sf_angle_restrict_pos
>
1654 =item C
<gsl_sf_angle_restrict_symm_err_e
>
1656 =item C
<gsl_sf_angle_restrict_pos_err_e
>
1658 =item C
<gsl_sf_atanint_e
>
1660 =item C
<gsl_sf_atanint
>
1662 =item C
<gsl_sf_zeta_int_e
>
1664 =item C
<gsl_sf_zeta_int
>
1666 =item C
<gsl_sf_zeta_e gsl_sf_zeta
>
1668 =item C
<gsl_sf_zetam1_e
>
1670 =item C
<gsl_sf_zetam1
>
1672 =item C
<gsl_sf_zetam1_int_e
>
1674 =item C
<gsl_sf_zetam1_int
>
1676 =item C
<gsl_sf_hzeta_e
>
1678 =item C
<gsl_sf_hzeta
>
1680 =item C
<gsl_sf_eta_int_e
>
1682 =item C
<gsl_sf_eta_int
>
1684 =item C
<gsl_sf_eta_e
>
1686 =item C
<gsl_sf_eta
>
1690 You can import the functions that you want to use by giving a space separated list to Math
::GSL
::SF when you use the package.
1691 You can also write use Math
::GSL
::SF qw
/:all
/ to use all avaible functions of the module. Note that the tag names begin with a colon.
1692 Other tags are also available
, here is a complete list of all tags for this module
:
1722 =item C
<hypergeometric
>
1742 For more informations on the functions
, we refer you to the GSL offcial
1743 documentation
: http
://www.gnu.org
/software
/gsl
/manual
/html_node
/
1745 Tip
: search on google
: site
:http
://www.gnu.org
/software
/gsl
/manual
/html_node
/name_of_the_function_you_want
1749 This example computes the dilogarithm of
1/10 :
1751 use Math
::GSL
::SF qw
/dilog
/;
1752 my $x
= gsl_sf_dilog
(0.1);
1753 print
"gsl_sf_dilog(0.1) = $x\n";
1755 An example using Math
::GSL
::SF and gnuplot is in the B
<examples
/sf
> folder of the source code.
1759 Jonathan Leto
<jonathan@leto.net
> and Thierry Moisan
<thierry.moisan@gmail.com
>
1761 =head1 COPYRIGHT
AND LICENSE
1763 Copyright
(C
) 2008 Jonathan Leto and Thierry Moisan
1765 This program is free software
; you can redistribute it and
/or modify it
1766 under the same terms as Perl itself.