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Zbl 0985.85002
Gong, Zhigang; Zejda, Ladislav; Däppen, Werner; Aparicio, Josep M.
Generalized Fermi-Dirac functions and derivatives: Properties and evaluation. (English)
[J] Comput. Phys. Commun. 136, No.3, 294-309 (2001). ISSN 0010-4655

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 {\it 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 2000:: *85A15 Galactic and stellar structure
85-08 Computational methods (astronomy and astrophysics)

Keywords: equation of state; electron gas; numerical method; hot dense stellar plasmas; Fortran program

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