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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).