Class fermi_dirac_integ_tl (o2scl)

O2scl : Class List

template<class inte_t, class fp_t = double>
class fermi_dirac_integ_tl

Compute a Fermi-Dirac integral by direct integration.

This class performs direct computation of the Fermi-Dirac integral

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

using an integrator which is specified as a class template parameter. This class is used in o2scl::fermi_dirac_integ_direct and o2scl::polylog .

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

Todo

In fermi_dirac_integ_tl, better testing of accuracy.

Public Functions

inline int calc_err(fp_t a, fp_t mu, fp_t &res, fp_t &err)

Compute the integral, storing the result in res and the error in err.

Public Members

inte_t iiu

The integrator.

Protected Types

typedef std::function<fp_t(fp_t)> func_t

Internal function type.

Protected Functions

inline fp_t obj_func(fp_t x, fp_t a, fp_t mu)

The Fermi-Dirac function.