Rational function approximations for Fermi-Dirac integrals

Antia, H. M. (1993) Rational function approximations for Fermi-Dirac integrals Astrophysical Journal Supplement Series, 84 . pp. 101-108. ISSN 0067-0049

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Official URL: http://articles.adsabs.harvard.edu//full/1993ApJS....

Abstract

Rational function minimax approximations are given for the complete Fermi-Dirac integrals of orders -½, ½, 3/2, and 5/2. In each case, three sets of approximations are provided with maximum relative error ≈ 10-4, 10-8, and 10-12, 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 ≈ 10-4 and 10-8 are also obtained.

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