Rational Function Approximations for Fermi-Dirac Integrals

Abstract

Rational function minimax approximations are given for the complete Fermi-Dirac integrals of orders -1, 1, and 1. In each case, three sets of approximations are provided with maximum relative error 1e-4, 1e-8, and 1e-12, respectively. These approximations can be used to compute the Fermi-Dirac integrals efficiently over the entire range. Approximations to the corresponding inverse functions with an accuracy of 1e-4 and 1e-8 are also obtained.