Rational Function Approximations for Fermi-Dirac Integrals

Details Rational Function Approximations for Fermi-Dirac Integrals Rational Function Approximations for Fermi-Dirac Integrals

Jan 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apjs...84..101a&link_type=abstract

Astrophysical Journal Supplement v.84, p.101

Astronomy and Astrophysics

Astronomy

22

Atomic Processes, Methods: Analytical

Scientific paper

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.

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