Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for Arbitrary Degeneracy and Relativity

Details Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for Arbitrary Degeneracy and Relativity Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for Arbitrary Degeneracy and Relativity

1995-09-25

arxiv.org/abs/astro-ph/9509124v1

Astronomy and Astrophysics

Astrophysics

AAS LaTeX. No Figures

Scientific paper

10.1086/192322

The equation of state of an ideal Fermi gas is expressed in terms of Fermi-Dirac integrals. We give formulae for evaluation the Fermi-Dirac integrals of orders 1/2, 3/2, and 5/2 and their derivatives in various limits of non- and extreme degeneracy and relativity. We provide tables and a Fortran subroutine for numerical evaluation of the integrals and derivatives when a limit does not apply. The functions can be evaluated to better than 1% accuracy for any temperature and density using these methods.

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