1FERMI_DIRAC(3)        User Contributed Perl Documentation       FERMI_DIRAC(3)
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NAME

6       PDL::GSLSF::FERMI_DIRAC - PDL interface to GSL Special Functions
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DESCRIPTION

9       This is an interface to the Special Function package present in the GNU
10       Scientific Library.  Please note that:
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12       Complete Fermi-Dirac Integrals:
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14        F_j(x)   := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,0,Infinity}]
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16       Incomplete Fermi-Dirac Integrals:
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18        F_j(x,b) := 1/Gamma[j+1] Integral[ t^j /(Exp[t-x] + 1), {t,b,Infinity}]
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SYNOPSIS

FUNCTIONS

22   gsl_sf_fermi_dirac_int
23         Signature: (double x(); double [o]y(); double [o]e(); int j)
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25       Complete integral F_j(x) for integer j
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27       gsl_sf_fermi_dirac_int does not process bad values.  It will set the
28       bad-value flag of all output piddles if the flag is set for any of the
29       input piddles.
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31   gsl_sf_fermi_dirac_mhalf
32         Signature: (double x(); double [o]y(); double [o]e())
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34       Complete integral F_{-1/2}(x)
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36       gsl_sf_fermi_dirac_mhalf does not process bad values.  It will set the
37       bad-value flag of all output piddles if the flag is set for any of the
38       input piddles.
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40   gsl_sf_fermi_dirac_half
41         Signature: (double x(); double [o]y(); double [o]e())
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43       Complete integral F_{1/2}(x)
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45       gsl_sf_fermi_dirac_half does not process bad values.  It will set the
46       bad-value flag of all output piddles if the flag is set for any of the
47       input piddles.
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49   gsl_sf_fermi_dirac_3half
50         Signature: (double x(); double [o]y(); double [o]e())
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52       Complete integral F_{3/2}(x)
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54       gsl_sf_fermi_dirac_3half does not process bad values.  It will set the
55       bad-value flag of all output piddles if the flag is set for any of the
56       input piddles.
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58   gsl_sf_fermi_dirac_inc_0
59         Signature: (double x(); double [o]y(); double [o]e(); double b)
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61       Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)
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63       gsl_sf_fermi_dirac_inc_0 does not process bad values.  It will set the
64       bad-value flag of all output piddles if the flag is set for any of the
65       input piddles.
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AUTHOR

68       This file copyright (C) 1999 Christian Pellegrin
69       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
70       You are allowed to redistribute this software / documentation under
71       certain conditions. For details, see the file COPYING in the PDL
72       distribution. If this file is separated from the PDL distribution, the
73       copyright notice should be included in the file.
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75       The GSL SF modules were written by G. Jungman.
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79perl v5.32.0                      2020-09-17                    FERMI_DIRAC(3)