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

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_int does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

gsl_sf_fermi_dirac_mhalf

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

Complete integral F_{-1/2}(x)

gsl_sf_fermi_dirac_mhalf does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

gsl_sf_fermi_dirac_half

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

Complete integral F_{1/2}(x)

gsl_sf_fermi_dirac_half does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

gsl_sf_fermi_dirac_3half

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

Complete integral F_{3/2}(x)

gsl_sf_fermi_dirac_3half does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

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)

gsl_sf_fermi_dirac_inc_0 does not process bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.


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.