FERMI_DIRAC(3) User Contributed Perl Documentation FERMI_DIRAC(3)NAME
PDL::GSLSF::FERMI_DIRAC - PDL interface to GSL Special Functions
DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library. Please note that:
Complete Fermi-Dirac Integrals:
F_j(x) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]
Incomplete Fermi-Dirac Integrals:
F_j(x,b) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,b,Infinity}]
SYNOPSIS FunctionsFUNCTIONS
gsl_sf_fermi_dirac_int
Signature: (double x(); double [o]y(); double [o]e(); int j)
Complete integral F_j(x) for integer j
gsl_sf_fermi_dirac_mhalf
Signature: (double x(); double [o]y(); double [o]e())
Complete integral F_{-1/2}(x)
gsl_sf_fermi_dirac_half
Signature: (double x(); double [o]y(); double [o]e())
Complete integral F_{1/2}(x)
gsl_sf_fermi_dirac_3half
Signature: (double x(); double [o]y(); double [o]e())
Complete integral F_{3/2}(x)
gsl_sf_fermi_dirac_inc_0
Signature: (double x(); double [o]y(); double [o]e(); double b)
Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)
AUTHOR
This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to
redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this
file is separated from the PDL distribution, the copyright notice should be included in the file.
The GSL SF modules were written by G. Jungman.
perl v5.8.0 2003-01-29 FERMI_DIRAC(3)
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HYPERG(3) User Contributed Perl Documentation HYPERG(3)NAME
PDL::GSLSF::HYPERG - PDL interface to GSL Special Functions
DESCRIPTION
This is an interface to the Special Function package present in the GNU Scientific Library.
SYNOPSIS FunctionsFUNCTIONS
gsl_sf_hyperg_0F1
Signature: (double x(); double [o]y(); double [o]e(); double c)
/* 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])
gsl_sf_hyperg_1F1
Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
Confluent hypergeometric function for integer parameters. 1F1[a,b,x] = M(a,b,x)
gsl_sf_hyperg_U
Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
Confluent hypergeometric function for integer parameters. U(a,b,x)
gsl_sf_hyperg_2F1
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Confluent hypergeometric function for integer parameters. 2F1[a,b,c,x]
gsl_sf_hyperg_2F1_conj
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x]
gsl_sf_hyperg_2F1_renorm
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Renormalized Gauss hypergeometric function 2F1[a,b,c,x] / Gamma[c]
gsl_sf_hyperg_2F1_conj_renorm
Signature: (double x(); double [o]y(); double [o]e(); double a; double b; double c)
Renormalized Gauss hypergeometric function 2F1[aR + I aI, aR - I aI, c, x] / Gamma[c]
gsl_sf_hyperg_2F0
Signature: (double x(); double [o]y(); double [o]e(); double a; double b)
Mysterious hypergeometric function. The series representation is a divergent hypergeometric series. However, for x < 0 we have 2F0(a,b,x) =
(-1/x)^a U(a,1+a-b,-1/x)
AUTHOR
This file copyright (C) 1999 Christian Pellegrin <chri@infis.univ.trieste.it> All rights reserved. There is no warranty. You are allowed to
redistribute this software / documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this
file is separated from the PDL distribution, the copyright notice should be included in the file.
The GSL SF modules were written by G. Jungman.
perl v5.8.0 2003-01-29 HYPERG(3)