Class fermi_dirac_integ_gsl (o2scl)

O2scl : Class List

class o2scl::fermi_dirac_integ_gsl

Compute the fermion integrals for a non-relativistic particle using the GSL functions.

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.

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

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

double calc_1o2(double y)

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

double calc_m1o2(double y)

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

double calc_3o2(double y)

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

double calc_2(double y)

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

double calc_3(double y)

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