Numerical calculation of the generalized Fermi-Dirac integrals

Abstract

The aim of this paper is to provide the best compromise between accuracy and CPU-time for calculating the generalized Fermi-Dirac integrals. After a brief review of the existing methods, with emphasis on two of them, we present our method valid for all values of the degeneracy parameter and of the temperature, with an accuracy in the range 10 -5–10 -7 and a short CPU-time. We have taken care of the computer implementation (including round-off errors, underflows or overflows) and we give the weights and abcissas of the Gauss-Laguerre quadrature rule needed for an accuracy of ϵ = 10 -6.