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Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. (English) Zbl 0985.85002
Summary: 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 J. M. Aparicio [Astrophys. J. Suppl. 117, 627-632 (1998)]. 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 of extreme conditions are investigated and compared with our results.
MSC:
85A15Galactic and stellar structure
85-08Computational methods (astronomy and astrophysics)