The accurate evaluation of a particular Fermi-Dirac integral

Abstract

In this paper, we provide a simple and very accurate numerical method to evaluate a particular two-dimensional Fermi-Dirac integral that arises in the plasma transport theory. The proposed method involves suitable coordinate and variable transformations which eliminate variable limits of integration. The resulting inner integral is evaluated by a trapezoidal integration with pole correction. The outer integral is evaluated by the IMT scheme. We provide reasonable error bounds. The results agree very well with the results of Fullerton and Rinker, who employ a combination of quadrature, asymptotic methods and Chebyshev fitting.