Rational Function Approximations for FermiDirac Integrals
Abstract
Rational function minimax approximations are given for the complete FermiDirac integrals of orders ½, ½, 3/2, and 5/2. In each case, three sets of approximations are provided with maximum relative error ≈ l0^{4}, 10^{8}, and 10^{12}, respectively. These approximations can be used to compute the FermiDirac integrals efficiently over the entire range. Approximations to the corresponding inverse functions with an accuracy of ≈l0^{4} and 10^{8} are also obtained.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 January 1993
 DOI:
 10.1086/191748
 Bibcode:
 1993ApJS...84..101A
 Keywords:

 atomic processes;
 methods: analytical