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 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

Functions
FUNCTIONS

       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)

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

NAME

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

DESCRIPTION

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

SYNOPSIS

Functions
FUNCTIONS

       gsl_sf_expint_E1

	 Signature: (double x(); double [o]y(); double [o]e())

       E_1(x) := Re[ Integrate[ Exp[-xt]/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[-t]/t, {t,-x,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}]

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								 EXPINT(3)