# pdl::gslsf::fermi_dirac(3) [redhat man page]

FERMI_DIRAC(3) User Contributed Perl Documentation FERMI_DIRAC(3)NAME

PDL::GSLSF::FERMI_DIRAC - PDL interface to GSL Special FunctionsDESCRIPTION

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 v5.8.02003-01-29 FERMI_DIRAC(3)

## Check Out this Related Man Page

EXPINT(3) User Contributed Perl Documentation EXPINT(3)NAME

PDL::GSLSF::EXPINT - PDL interface to GSL Special FunctionsDESCRIPTION

This is an interface to the Special Function package present in the GNU Scientific Library.SYNOPSIS

FunctionsFUNCTIONS

gsl_sf_expint_E1 Signature: (double x(); double [o]y(); double [o]e()) E_1(x) := Re[ Integrate[ Exp[]/t, {t,1,Infinity}] ] gsl_sf_expint_E2 Signature: (double x(); double [o]y(); double [o]e()) E_2(x) := Re[ Integrate[ Exp[-xt]/t^2, {t,1,Infity}] ] gsl_sf_expint_Ei Signature: (double x(); double [o]y(); double [o]e()) Ei(x) := PV Integrate[ Exp[-xt]/t, {t,-t,Infinity}] gsl_sf_Shi Signature: (double x(); double [o]y(); double [o]e()) Shi(x) := Integrate[ Sinh[t]/t, {t,0,x}] gsl_sf_Chi Signature: (double x(); double [o]y(); double [o]e()) Chi(x) := Re[ M_EULER + log(x) + Integrate[(Cosh[t]-1)/t, {t,0,x}] ] gsl_sf_expint_3 Signature: (double x(); double [o]y(); double [o]e()) Ei_3(x) := Integral[ Exp[-t^3], {t,0,x}] gsl_sf_Si Signature: (double x(); double [o]y(); double [o]e()) Si(x) := Integrate[ Sin[t]/t, {t,0,x}] gsl_sf_Ci Signature: (double x(); double [o]y(); double [o]e()) Ci(x) := -Integrate[ Cos[t]/t, {t,x,Infinity}] gsl_sf_atanint Signature: (double x(); double [o]y(); double [o]e()) AtanInt(x) := Integral[ Arctan[t]/t, {t,0,x}]-xAUTHOR

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 v5.8.02003-01-29 EXPINT(3)