Generalized Fermi–Dirac functions and derivatives: properties and evaluation

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 [Ap.J.S.S. 117 (1998) 627]. A Fo... Title of program: GFD_D3 Catalogue Id: ADNX_v1_0 Nature of problem Provide numerical method to evaluate generalized Fermi-Dirac functions and their derivatives with respect to eta and beta up to third order. The results are important for a highly accurate calculation of thermodynamic quantities of an electron gas with partial degeneracy and relatively high temperatures with very high order of accuracy. Versions of this program held in the CPC repository in Mendeley Data ADNX_v1_0; GFD_D3; 10.1016/S0010-4655(01)00145-X This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)