On the very accurate numerical evaluation of the Generalized Fermi-Dirac Integrals

We indicate a new and a very accurate algorithm for the evaluation of the Generalized Fermi-Dirac Integral with a relative error less than 10−20. The method involves Double Exponential, Trapezoidal and Gauss-Legendre quadratures. For the residue correction of the Gauss-Legendre scheme, a simple and precise continued fraction algorithm is used.