7.18.2 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).