1ELLINT(3)             User Contributed Perl Documentation            ELLINT(3)
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NAME

6       PDL::GSLSF::ELLINT - PDL interface to GSL Special Functions
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DESCRIPTION

9       This is an interface to the Special Function package present in the GNU
10       Scientific Library.
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FUNCTIONS

13   gsl_sf_ellint_Kcomp
14         Signature: (double k(); double [o]y(); double [o]e())
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16       Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 -
17       k^2 Sin[t]^2], {t, 0, Pi/2}].
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19       gsl_sf_ellint_Kcomp does not process bad values.  It will set the bad-
20       value flag of all output ndarrays if the flag is set for any of the
21       input ndarrays.
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23   gsl_sf_ellint_Ecomp
24         Signature: (double k(); double [o]y(); double [o]e())
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26       Legendre form of complete elliptic integrals E(k) = Integral[  Sqrt[1 -
27       k^2 Sin[t]^2], {t, 0, Pi/2}]
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29       gsl_sf_ellint_Ecomp does not process bad values.  It will set the bad-
30       value flag of all output ndarrays if the flag is set for any of the
31       input ndarrays.
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33   gsl_sf_ellint_F
34         Signature: (double phi(); double k(); double [o]y(); double [o]e())
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36       Legendre form of incomplete elliptic integrals F(phi,k)   =
37       Integral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
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39       gsl_sf_ellint_F does not process bad values.  It will set the bad-value
40       flag of all output ndarrays if the flag is set for any of the input
41       ndarrays.
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43   gsl_sf_ellint_E
44         Signature: (double phi(); double k(); double [o]y(); double [o]e())
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46       Legendre form of incomplete elliptic integrals E(phi,k)   = Integral[
47       Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
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49       gsl_sf_ellint_E does not process bad values.  It will set the bad-value
50       flag of all output ndarrays if the flag is set for any of the input
51       ndarrays.
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53   gsl_sf_ellint_P
54         Signature: (double phi(); double k(); double n();
55                     double [o]y(); double [o]e())
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57       Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral[(1
58       + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
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60       gsl_sf_ellint_P does not process bad values.  It will set the bad-value
61       flag of all output ndarrays if the flag is set for any of the input
62       ndarrays.
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64   gsl_sf_ellint_D
65         Signature: (double phi(); double k();
66                     double [o]y(); double [o]e())
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68       Legendre form of incomplete elliptic integrals D(phi,k)
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70       gsl_sf_ellint_D does not process bad values.  It will set the bad-value
71       flag of all output ndarrays if the flag is set for any of the input
72       ndarrays.
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74   gsl_sf_ellint_RC
75         Signature: (double x(); double yy(); double [o]y(); double [o]e())
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77       Carlsons symmetric basis of functions RC(x,y)   = 1/2
78       Integral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}
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80       gsl_sf_ellint_RC does not process bad values.  It will set the bad-
81       value flag of all output ndarrays if the flag is set for any of the
82       input ndarrays.
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84   gsl_sf_ellint_RD
85         Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
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87       Carlsons symmetric basis of functions RD(x,y,z) = 3/2
88       Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]
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90       gsl_sf_ellint_RD does not process bad values.  It will set the bad-
91       value flag of all output ndarrays if the flag is set for any of the
92       input ndarrays.
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94   gsl_sf_ellint_RF
95         Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
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97       Carlsons symmetric basis of functions RF(x,y,z) = 1/2
98       Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]
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100       gsl_sf_ellint_RF does not process bad values.  It will set the bad-
101       value flag of all output ndarrays if the flag is set for any of the
102       input ndarrays.
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104   gsl_sf_ellint_RJ
105         Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())
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107       Carlsons symmetric basis of functions RJ(x,y,z,p) = 3/2
108       Integral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]
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110       gsl_sf_ellint_RJ does not process bad values.  It will set the bad-
111       value flag of all output ndarrays if the flag is set for any of the
112       input ndarrays.
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AUTHOR

115       This file copyright (C) 1999 Christian Pellegrin
116       <chri@infis.univ.trieste.it>, 2002 Christian Soeller.  All rights
117       reserved. There is no warranty. You are allowed to redistribute this
118       software / documentation under certain conditions. For details, see the
119       file COPYING in the PDL distribution. If this file is separated from
120       the PDL distribution, the copyright notice should be included in the
121       file.
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123       The GSL SF modules were written by G. Jungman.
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127perl v5.36.0                      2023-01-20                         ELLINT(3)