HYPERG.pm (PDL-2.081) | : | HYPERG.pm (PDL-2.082) | ||
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skipping to change at line 37 | skipping to change at line 37 | |||

This is an interface to the Special Function package present in the GNU Scientif ic Library. | This is an interface to the Special Function package present in the GNU Scientif ic Library. | |||

=cut | =cut | |||

#line 39 "HYPERG.pm" | #line 39 "HYPERG.pm" | |||

=head1 FUNCTIONS | =head1 FUNCTIONS | |||

=cut | =cut | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_0F1 | =head2 gsl_sf_hyperg_0F1 | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double c) | Signature: (double x(); double [o]y(); double [o]e(); double c) | |||

=for ref | =for ref | |||

/* Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^ (1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x]) | /* Hypergeometric function related to Bessel functions 0F1[c,x] = Gamma[c] x^ (1/2(1-c)) I_{c-1}(2 Sqrt[x]) Gamma[c] (-x)^(1/2(1-c)) J_{c-1}(2 Sqrt[-x]) | |||

=for bad | =for bad | |||

gsl_sf_hyperg_0F1 does not process bad values. | gsl_sf_hyperg_0F1 does not process bad values. | |||

It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. | ||||

=cut | =cut | |||

#line 74 "HYPERG.pm" | #line 74 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_0F1 = \&PDL::gsl_sf_hyperg_0F1; | *gsl_sf_hyperg_0F1 = \&PDL::gsl_sf_hyperg_0F1; | |||

#line 81 "HYPERG.pm" | #line 81 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_1F1 | =head2 gsl_sf_hyperg_1F1 | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b) | |||

=for ref | =for ref | |||

Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x) | Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x) | |||

=for bad | =for bad | |||

gsl_sf_hyperg_1F1 does not process bad values. | gsl_sf_hyperg_1F1 does not process bad values. | |||

=cut | =cut | |||

#line 106 "HYPERG.pm" | #line 106 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_1F1 = \&PDL::gsl_sf_hyperg_1F1; | *gsl_sf_hyperg_1F1 = \&PDL::gsl_sf_hyperg_1F1; | |||

#line 113 "HYPERG.pm" | #line 113 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_U | =head2 gsl_sf_hyperg_U | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b) | |||

=for ref | =for ref | |||

Confluent hypergeometric function for integer parameters. U(a,b,x) | Confluent hypergeometric function for integer parameters. U(a,b,x) | |||

=for bad | =for bad | |||

gsl_sf_hyperg_U does not process bad values. | gsl_sf_hyperg_U does not process bad values. | |||

=cut | =cut | |||

#line 138 "HYPERG.pm" | #line 138 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_U = \&PDL::gsl_sf_hyperg_U; | *gsl_sf_hyperg_U = \&PDL::gsl_sf_hyperg_U; | |||

#line 145 "HYPERG.pm" | #line 145 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_2F1 | =head2 gsl_sf_hyperg_2F1 | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | |||

=for ref | =for ref | |||

Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x] | Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x] | |||

=for bad | =for bad | |||

gsl_sf_hyperg_2F1 does not process bad values. | gsl_sf_hyperg_2F1 does not process bad values. | |||

=cut | =cut | |||

#line 170 "HYPERG.pm" | #line 170 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_2F1 = \&PDL::gsl_sf_hyperg_2F1; | *gsl_sf_hyperg_2F1 = \&PDL::gsl_sf_hyperg_2F1; | |||

#line 177 "HYPERG.pm" | #line 177 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_2F1_conj | =head2 gsl_sf_hyperg_2F1_conj | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | |||

=for ref | =for ref | |||

Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] | Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] | |||

=for bad | =for bad | |||

gsl_sf_hyperg_2F1_conj does not process bad values. | gsl_sf_hyperg_2F1_conj does not process bad values. | |||

=cut | =cut | |||

#line 202 "HYPERG.pm" | #line 202 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_2F1_conj = \&PDL::gsl_sf_hyperg_2F1_conj; | *gsl_sf_hyperg_2F1_conj = \&PDL::gsl_sf_hyperg_2F1_conj; | |||

#line 209 "HYPERG.pm" | #line 209 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_2F1_renorm | =head2 gsl_sf_hyperg_2F1_renorm | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | |||

=for ref | =for ref | |||

Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c] | Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c] | |||

=for bad | =for bad | |||

gsl_sf_hyperg_2F1_renorm does not process bad values. | gsl_sf_hyperg_2F1_renorm does not process bad values. | |||

=cut | =cut | |||

#line 234 "HYPERG.pm" | #line 234 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_2F1_renorm = \&PDL::gsl_sf_hyperg_2F1_renorm; | *gsl_sf_hyperg_2F1_renorm = \&PDL::gsl_sf_hyperg_2F1_renorm; | |||

#line 241 "HYPERG.pm" | #line 241 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_2F1_conj_renorm | =head2 gsl_sf_hyperg_2F1_conj_renorm | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b; doub le c) | |||

=for ref | =for ref | |||

Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gam ma[c] | Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gam ma[c] | |||

=for bad | =for bad | |||

gsl_sf_hyperg_2F1_conj_renorm does not process bad values. | gsl_sf_hyperg_2F1_conj_renorm does not process bad values. | |||

=cut | =cut | |||

#line 266 "HYPERG.pm" | #line 266 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_2F1_conj_renorm = \&PDL::gsl_sf_hyperg_2F1_conj_renorm; | *gsl_sf_hyperg_2F1_conj_renorm = \&PDL::gsl_sf_hyperg_2F1_conj_renorm; | |||

#line 273 "HYPERG.pm" | #line 273 "HYPERG.pm" | |||

#line 949 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 958 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

=head2 gsl_sf_hyperg_2F0 | =head2 gsl_sf_hyperg_2F0 | |||

=for sig | =for sig | |||

Signature: (double x(); double [o]y(); double [o]e(); double a; double b) | Signature: (double x(); double [o]y(); double [o]e(); double a; double b) | |||

=for ref | =for ref | |||

Mysterious hypergeometric function. The series representation is a divergent hyp ergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,- 1/x) | Mysterious hypergeometric function. The series representation is a divergent hyp ergeometric series. However, for x < 0 we have 2F0(a,b,x) = (-1/x)^a U(a,1+a-b,- 1/x) | |||

=for bad | =for bad | |||

gsl_sf_hyperg_2F0 does not process bad values. | gsl_sf_hyperg_2F0 does not process bad values. | |||

=cut | =cut | |||

#line 298 "HYPERG.pm" | #line 298 "HYPERG.pm" | |||

#line 951 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | #line 960 "/home/osboxes/pdl-code/blib/lib/PDL/PP.pm" | |||

*gsl_sf_hyperg_2F0 = \&PDL::gsl_sf_hyperg_2F0; | *gsl_sf_hyperg_2F0 = \&PDL::gsl_sf_hyperg_2F0; | |||

#line 305 "HYPERG.pm" | #line 305 "HYPERG.pm" | |||

#line 130 "gsl_sf_hyperg.pd" | #line 130 "gsl_sf_hyperg.pd" | |||

=head1 AUTHOR | =head1 AUTHOR | |||

This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> | This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> | |||

All rights reserved. There | All rights reserved. There | |||

End of changes. 16 change blocks. | ||||

16 lines changed or deleted | | 16 lines changed or added |