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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FUNCTIONS

21   gsl_sf_fermi_dirac_int
22         Signature: (double x(); double [o]y(); double [o]e(); int j)
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24       Complete integral F_j(x) for integer j
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26       gsl_sf_fermi_dirac_int does not process bad values.  It will set the
27       bad-value flag of all output ndarrays if the flag is set for any of the
28       input ndarrays.
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30   gsl_sf_fermi_dirac_mhalf
31         Signature: (double x(); double [o]y(); double [o]e())
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33       Complete integral F_{-1/2}(x)
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35       gsl_sf_fermi_dirac_mhalf does not process bad values.  It will set the
36       bad-value flag of all output ndarrays if the flag is set for any of the
37       input ndarrays.
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39   gsl_sf_fermi_dirac_half
40         Signature: (double x(); double [o]y(); double [o]e())
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42       Complete integral F_{1/2}(x)
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44       gsl_sf_fermi_dirac_half does not process bad values.  It will set the
45       bad-value flag of all output ndarrays if the flag is set for any of the
46       input ndarrays.
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48   gsl_sf_fermi_dirac_3half
49         Signature: (double x(); double [o]y(); double [o]e())
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51       Complete integral F_{3/2}(x)
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53       gsl_sf_fermi_dirac_3half does not process bad values.  It will set the
54       bad-value flag of all output ndarrays if the flag is set for any of the
55       input ndarrays.
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57   gsl_sf_fermi_dirac_inc_0
58         Signature: (double x(); double [o]y(); double [o]e(); double b)
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60       Incomplete integral F_0(x,b) = ln(1 + e^(b-x)) - (b-x)
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62       gsl_sf_fermi_dirac_inc_0 does not process bad values.  It will set the
63       bad-value flag of all output ndarrays if the flag is set for any of the
64       input ndarrays.
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AUTHOR

67       This file copyright (C) 1999 Christian Pellegrin
68       <chri@infis.univ.trieste.it> All rights reserved. There is no warranty.
69       You are allowed to redistribute this software / documentation under
70       certain conditions. For details, see the file COPYING in the PDL
71       distribution. If this file is separated from the PDL distribution, the
72       copyright notice should be included in the file.
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74       The GSL SF modules were written by G. Jungman.
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78perl v5.34.0                      2022-02-28                    FERMI_DIRAC(3)
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