Generalized Fermi-Dirac functions and derivatives: properties and evaluation

The generalized Fermi-Dirac functions and their derivatives are important i n evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized F ermi-Dirac functions have been found. An effective numerical method to eval uate the derivatives of the generalized Fermi-Dirac functions up to third o rder with respect to both degeneracy and temperature is then proposed, foll owing Aparicio [Ap.J.S.S. 117 (1998) 627]. 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. (C) 2001 Elsevier Science B.V. All rights re served.