### Complete Fermi-Dirac Integrals

The complete Fermi-Dirac integral @math{F_j(x)} is given by,

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 @math{-1}. This integral is given by @math{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 @math{0}. This integral is given by @math{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 @math{1}, @math{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 @math{2}, @math{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 @math{j}, @math{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 @math{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 @math{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 @math{F_{3/2}(x)}.