Rational Function Approximations for Fermi-Dirac Integrals
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 ≈ l0-4, 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 ≈l0-4 and 10-8 are also obtained.
- Publication:
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The Astrophysical Journal Supplement Series
- Pub Date:
- January 1993
- DOI:
- Bibcode:
- 1993ApJS...84..101A
- Keywords:
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- atomic processes;
- methods: analytical