.\" Automatically generated by Pod::Man 4.14 (Pod::Simple 3.43) .\" .\" Standard preamble: .\" ======================================================================== .de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. .de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. .de Ve \" End verbatim text .ft R .fi .. .\" Set up some character translations and predefined strings. \*(-- will .\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left .\" double quote, and \*(R" will give a right double quote. \*(C+ will .\" give a nicer C++. Capital omega is used to do unbreakable dashes and .\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff, .\" nothing in troff, for use with C<>. .tr \(*W- .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' .ie n \{\ . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} .el\{\ . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\} .\" .\" Escape single quotes in literal strings from groff's Unicode transform. .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" .\" If the F register is >0, we'll generate index entries on stderr for .\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index .\" entries marked with X<> in POD. Of course, you'll have to process the .\" output yourself in some meaningful fashion. .\" .\" Avoid warning from groff about undefined register 'F'. .de IX .. .nr rF 0 .if \n(.g .if rF .nr rF 1 .if (\n(rF:(\n(.g==0)) \{\ . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF .\" ======================================================================== .\" .IX Title "ELLINT 3pm" .TH ELLINT 3pm "2023-06-17" "perl v5.36.0" "User Contributed Perl Documentation" .\" For nroff, turn off justification. Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .SH "NAME" PDL::GSLSF::ELLINT \- PDL interface to GSL Special Functions .SH "DESCRIPTION" .IX Header "DESCRIPTION" This is an interface to the Special Function package present in the \s-1GNU\s0 Scientific Library. .SH "FUNCTIONS" .IX Header "FUNCTIONS" .SS "gsl_sf_ellint_Kcomp" .IX Subsection "gsl_sf_ellint_Kcomp" .Vb 1 \& Signature: (double k(); double [o]y(); double [o]e()) .Ve .PP Legendre form of complete elliptic integrals K(k) = Integral[1/Sqrt[1 \- k^2 Sin[t]^2], {t, 0, Pi/2}]. .PP gsl_sf_ellint_Kcomp 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. .SS "gsl_sf_ellint_Ecomp" .IX Subsection "gsl_sf_ellint_Ecomp" .Vb 1 \& Signature: (double k(); double [o]y(); double [o]e()) .Ve .PP Legendre form of complete elliptic integrals E(k) = Integral[ Sqrt[1 \- k^2 Sin[t]^2], {t, 0, Pi/2}] .PP gsl_sf_ellint_Ecomp 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. .SS "gsl_sf_ellint_F" .IX Subsection "gsl_sf_ellint_F" .Vb 1 \& Signature: (double phi(); double k(); double [o]y(); double [o]e()) .Ve .PP Legendre form of incomplete elliptic integrals F(phi,k) = Integral[1/Sqrt[1 \- k^2 Sin[t]^2], {t, 0, phi}] .PP gsl_sf_ellint_F 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. .SS "gsl_sf_ellint_E" .IX Subsection "gsl_sf_ellint_E" .Vb 1 \& Signature: (double phi(); double k(); double [o]y(); double [o]e()) .Ve .PP Legendre form of incomplete elliptic integrals E(phi,k) = Integral[ Sqrt[1 \- k^2 Sin[t]^2], {t, 0, phi}] .PP gsl_sf_ellint_E 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. .SS "gsl_sf_ellint_P" .IX Subsection "gsl_sf_ellint_P" .Vb 2 \& Signature: (double phi(); double k(); double n(); \& double [o]y(); double [o]e()) .Ve .PP Legendre form of incomplete elliptic integrals P(phi,k,n) = Integral[(1 + n Sin[t]^2)^(\-1)/Sqrt[1 \- k^2 Sin[t]^2], {t, 0, phi}] .PP gsl_sf_ellint_P 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. .SS "gsl_sf_ellint_D" .IX Subsection "gsl_sf_ellint_D" .Vb 2 \& Signature: (double phi(); double k(); \& double [o]y(); double [o]e()) .Ve .PP Legendre form of incomplete elliptic integrals D(phi,k) .PP gsl_sf_ellint_D 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. .SS "gsl_sf_ellint_RC" .IX Subsection "gsl_sf_ellint_RC" .Vb 1 \& Signature: (double x(); double yy(); double [o]y(); double [o]e()) .Ve .PP Carlsons symmetric basis of functions \s-1RC\s0(x,y) = 1/2 Integral[(t+x)^(\-1/2) (t+y)^(\-1)], {t,0,Inf} .PP gsl_sf_ellint_RC 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. .SS "gsl_sf_ellint_RD" .IX Subsection "gsl_sf_ellint_RD" .Vb 1 \& Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e()) .Ve .PP Carlsons symmetric basis of functions \s-1RD\s0(x,y,z) = 3/2 Integral[(t+x)^(\-1/2) (t+y)^(\-1/2) (t+z)^(\-3/2), {t,0,Inf}] .PP gsl_sf_ellint_RD 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. .SS "gsl_sf_ellint_RF" .IX Subsection "gsl_sf_ellint_RF" .Vb 1 \& Signature: (double x(); double yy(); double z(); double [o]y(); double [o]e()) .Ve .PP Carlsons symmetric basis of functions \s-1RF\s0(x,y,z) = 1/2 Integral[(t+x)^(\-1/2) (t+y)^(\-1/2) (t+z)^(\-1/2), {t,0,Inf}] .PP gsl_sf_ellint_RF 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. .SS "gsl_sf_ellint_RJ" .IX Subsection "gsl_sf_ellint_RJ" .Vb 1 \& Signature: (double x(); double yy(); double z(); double p(); double [o]y(); double [o]e()) .Ve .PP Carlsons symmetric basis of functions \s-1RJ\s0(x,y,z,p) = 3/2 Integral[(t+x)^(\-1/2) (t+y)^(\-1/2) (t+z)^(\-1/2) (t+p)^(\-1), {t,0,Inf}] .PP gsl_sf_ellint_RJ 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. .SH "AUTHOR" .IX Header "AUTHOR" This file copyright (C) 1999 Christian Pellegrin , 2002 Christian Soeller. All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation under certain conditions. For details, see the file \&\s-1COPYING\s0 in the \s-1PDL\s0 distribution. If this file is separated from the \&\s-1PDL\s0 distribution, the copyright notice should be included in the file. .PP The \s-1GSL SF\s0 modules were written by G. Jungman.