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

Juan Antonio Miralles·Kenneth A. Van Riper
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Abstract

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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Juan Antonio Miralles, Kenneth A. Van Riper. 1995-09-25. Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for Arbitrary Degeneracy and Relativity. https://doi.org/10.1086/192322

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