Class fermi_dirac_integ_gsl (o2scl)

O2scl : Class List

class fermi_dirac_integ_gsl

Compute several Fermi-Dirac integrals useful for non-relativistic fermions using GSL.

This class performs direct computation of the Fermi-Dirac integral

\[ F_{a}(\mu) = \int_0^{\infty} \frac{x^a}{1+e^{x-\mu}} \, . \]

using the functions from GSL where \( a \in [-1/2,1/2,3/2,2,3] \) .

Note that the GSL definition of the Fermi-Dirac integral includes an additional factor of \( 1/\Gamma(a+1) \) which is not included here.

The GSL functions internally throw overflow exceptions if the argument is too large. In this class, the value inf is returned in those cases instead.

This class is used in in o2scl::fermion_thermo_tl, o2scl::fermion_tl and o2scl::fermion_nonrel_tl to compute the Fermi-Dirac integrals for non-relativistic fermions.

Public Functions

inline double calc_1o2(double y)

Fermi-Dirac integral of order \( 1/2 \).

inline double calc_m1o2(double y)

Fermi-Dirac integral of order \( -1/2 \).

inline double calc_3o2(double y)

Fermi-Dirac integral of order \( 3/2 \).

inline double calc_2(double y)

Fermi-Dirac integral of order \( 2 \).

inline double calc_3(double y)

Fermi-Dirac integral of order \( 3 \).