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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SYNOPSIS

Functions

FUNCTIONS

15       gsl_sf_ellint_Kcomp
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17         Signature: (double k(); double [o]y(); double [o]e())
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19       Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 -
20       k^2 Sin[t]^2], {t, 0, Pi/2}].
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22       gsl_sf_ellint_Ecomp
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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_F
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31         Signature: (double phi(); double k(); double [o]y(); double [o]e())
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33       Legendre form of incomplete elliptic integrals F(phi,k)   = Inte‐
34       gral[1/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
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36       gsl_sf_ellint_E
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38         Signature: (double phi(); double k(); double [o]y(); double [o]e())
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40       Legendre form of incomplete elliptic integrals E(phi,k)   = Integral[
41       Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
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43       gsl_sf_ellint_P
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45         Signature: (double phi(); double k(); double n();
46                     double [o]y(); double [o]e())
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48       Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral[(1
49       + n Sin[t]^2)^(-1)/Sqrt[1 - k^2 Sin[t]^2], {t, 0, phi}]
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51       gsl_sf_ellint_D
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53         Signature: (double phi(); double k(); double n();
54                     double [o]y(); double [o]e())
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56       Legendre form of incomplete elliptic integrals D(phi,k,n)
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58       gsl_sf_ellint_RC
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60         Signature: (double x(); double yy(); double [o]y(); double [o]e())
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62       Carlsons symmetric basis of functions RC(x,y)   = 1/2 Inte‐
63       gral[(t+x)^(-1/2) (t+y)^(-1)], {t,0,Inf}
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65       gsl_sf_ellint_RD
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67         Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
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69       Carlsons symmetric basis of functions RD(x,y,z) = 3/2 Inte‐
70       gral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2), {t,0,Inf}]
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72       gsl_sf_ellint_RF
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74         Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e())
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76       Carlsons symmetric basis of functions RF(x,y,z) = 1/2 Inte‐
77       gral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2), {t,0,Inf}]
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79       gsl_sf_ellint_RJ
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81         Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e())
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83       Carlsons symmetric basis of functions RJ(x,y,z,p) = 3/2 Inte‐
84       gral[(t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1), {t,0,Inf}]
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AUTHOR

87       This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.tri‐
88       este.it>, 2002 Christian Soeller.  All rights reserved. There is no
89       warranty. You are allowed to redistribute this software / documentation
90       under certain conditions. For details, see the file COPYING in the PDL
91       distribution. If this file is separated from the PDL distribution, the
92       copyright notice should be included in the file.
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94       The GSL SF modules were written by G. Jungman.
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98perl v5.8.8                       2006-12-02                         ELLINT(3)