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Generalized Fermi-Dirac Functions and Derivatives: Properties and Evaluation

Zhigang Gong·Ladislav Zejda·Werner Dappen·Josep M. Aparicio
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Abstract

The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac functions have been found. An effective numerical method to evaluate the derivatives of the generalized Fermi-Dirac functions up to third order with respect to both degeneracy and temperature is then proposed, following Aparicio. A Fortran program based on this method, together with a sample test case, is provided. Accuracy and domain of reliability of some other, popularly used analytic approximations of the generalized Fermi-Dirac functions for extreme conditions are investigated and compared with our results.

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Zhigang Gong, Ladislav Zejda, Werner Dappen, Josep M. Aparicio. 2001-02-20. Generalized Fermi-Dirac Functions and Derivatives: Properties and Evaluation. https://doi.org/10.1016/s0010-4655(01)00145-x

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