The functions described in this section are declared in the header file gsl_sf_fermi_dirac.h.

Complete Fermi-Dirac Integrals
------------------------------

The complete Fermi-Dirac integral F_j(x) is given by,

     F_j(x)   := (1/r\Gamma(j+1)) \int_0^\infty dt (t^j / (\exp(t-x) + 1))

 -- Function: double gsl_sf_fermi_dirac_m1 (double X)
 -- Function: int gsl_sf_fermi_dirac_m1_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral with an index of -1. This integral is given by $F_-1(x) = e^x / (1 + e^x)$ F_{-1}(x) = e^x / (1 + e^x).

 -- Function: double gsl_sf_fermi_dirac_0 (double X)
 -- Function: int gsl_sf_fermi_dirac_0_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral with an index of 0. This integral is given by F_0(x) = \ln(1 + e^x).

 -- Function: double gsl_sf_fermi_dirac_1 (double X)
 -- Function: int gsl_sf_fermi_dirac_1_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral with an index of 1, F_1(x) = \int_0^\infty dt (t /(\exp(t-x)+1)).

 -- Function: double gsl_sf_fermi_dirac_2 (double X)
 -- Function: int gsl_sf_fermi_dirac_2_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) \int_0^\infty dt (t^2 /(\exp(t-x)+1)).

 -- Function: double gsl_sf_fermi_dirac_int (int J, double X)
 -- Function: int gsl_sf_fermi_dirac_int_e (int J, double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)).

 -- Function: double gsl_sf_fermi_dirac_mhalf (double X)
 -- Function: int gsl_sf_fermi_dirac_mhalf_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral $F_-1/2(x)$ F_{-1/2}(x).

 -- Function: double gsl_sf_fermi_dirac_half (double X)
 -- Function: int gsl_sf_fermi_dirac_half_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral $F_1/2(x)$ F_{1/2}(x).

 -- Function: double gsl_sf_fermi_dirac_3half (double X)
 -- Function: int gsl_sf_fermi_dirac_3half_e (double X, gsl_sf_result * RESULT)
     These routines compute the complete Fermi-Dirac integral $F_3/2(x)$ F_{3/2}(x).

Incomplete Fermi-Dirac Integrals
--------------------------------

The incomplete Fermi-Dirac integral F_j(x,b) is given by,

     F_j(x,b)   := (1/\Gamma(j+1)) \int_b^\infty dt (t^j / (\Exp(t-x) + 1))

 -- Function: double gsl_sf_fermi_dirac_inc_0 (double X, double B)
 -- Function: int gsl_sf_fermi_dirac_inc_0_e (double X, double B, gsl_sf_result * RESULT)
     These routines compute the incomplete Fermi-Dirac integral with an index of zero, $F_0(x,b) = \ln(1 + e^b-x) - (b-x)$ F_0(x,b) = \ln(1 + e^{b-x}) - (b-x).