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Diffstat (limited to 'gsl-1.9/doc/specfunc-fermi-dirac.texi')
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diff --git a/gsl-1.9/doc/specfunc-fermi-dirac.texi b/gsl-1.9/doc/specfunc-fermi-dirac.texi new file mode 100644 index 0000000..f9314be --- /dev/null +++ b/gsl-1.9/doc/specfunc-fermi-dirac.texi @@ -0,0 +1,122 @@ +@cindex Fermi-Dirac function + +The functions described in this section are declared in the header file +@file{gsl_sf_fermi_dirac.h}. + +@menu +* Complete Fermi-Dirac Integrals:: +* Incomplete Fermi-Dirac Integrals:: +@end menu + +@node Complete Fermi-Dirac Integrals +@subsection Complete Fermi-Dirac Integrals +@cindex complete Fermi-Dirac integrals +@cindex Fj(x), Fermi-Dirac integral +The complete Fermi-Dirac integral @math{F_j(x)} is given by, +@tex +\beforedisplay +$$ +F_j(x) := {1\over\Gamma(j+1)} \int_0^\infty dt {t^j \over (\exp(t-x) + 1)} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +F_j(x) := (1/r\Gamma(j+1)) \int_0^\infty dt (t^j / (\exp(t-x) + 1)) +@end example +@end ifinfo + +@deftypefun double gsl_sf_fermi_dirac_m1 (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_m1_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral with an index of @math{-1}. +This integral is given by +@c{$F_{-1}(x) = e^x / (1 + e^x)$} +@math{F_@{-1@}(x) = e^x / (1 + e^x)}. +@comment Exceptional Return Values: GSL_EUNDRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_0 (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_0_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral with an index of @math{0}. +This integral is given by @math{F_0(x) = \ln(1 + e^x)}. +@comment Exceptional Return Values: GSL_EUNDRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_1 (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_1_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral with an index of @math{1}, +@math{F_1(x) = \int_0^\infty dt (t /(\exp(t-x)+1))}. +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_2 (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_2_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral with an index +of @math{2}, +@math{F_2(x) = (1/2) \int_0^\infty dt (t^2 /(\exp(t-x)+1))}. +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_int (int @var{j}, double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_int_e (int @var{j}, double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral with an integer +index of @math{j}, +@math{F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1))}. +@comment Complete integral F_j(x) for integer j +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_mhalf (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_mhalf_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral +@c{$F_{-1/2}(x)$} +@math{F_@{-1/2@}(x)}. +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_half (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_half_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral +@c{$F_{1/2}(x)$} +@math{F_@{1/2@}(x)}. +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW +@end deftypefun + +@deftypefun double gsl_sf_fermi_dirac_3half (double @var{x}) +@deftypefunx int gsl_sf_fermi_dirac_3half_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the complete Fermi-Dirac integral +@c{$F_{3/2}(x)$} +@math{F_@{3/2@}(x)}. +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EOVRFLW +@end deftypefun + + +@node Incomplete Fermi-Dirac Integrals +@subsection Incomplete Fermi-Dirac Integrals +@cindex incomplete Fermi-Dirac integral +@cindex Fj(x,b), incomplete Fermi-Dirac integral +The incomplete Fermi-Dirac integral @math{F_j(x,b)} is given by, +@tex +\beforedisplay +$$ +F_j(x,b) := {1\over\Gamma(j+1)} \int_b^\infty dt {t^j \over (\exp(t-x) + 1)} +$$ +\afterdisplay +@end tex +@ifinfo + +@example +F_j(x,b) := (1/\Gamma(j+1)) \int_b^\infty dt (t^j / (\Exp(t-x) + 1)) +@end example +@end ifinfo + +@deftypefun double gsl_sf_fermi_dirac_inc_0 (double @var{x}, double @var{b}) +@deftypefunx int gsl_sf_fermi_dirac_inc_0_e (double @var{x}, double @var{b}, gsl_sf_result * @var{result}) +These routines compute the incomplete Fermi-Dirac integral with an index +of zero, +@c{$F_0(x,b) = \ln(1 + e^{b-x}) - (b-x)$} +@math{F_0(x,b) = \ln(1 + e^@{b-x@}) - (b-x)}. +@comment Exceptional Return Values: GSL_EUNDRFLW, GSL_EDOM +@end deftypefun + |