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. 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.
Cite
@article{arxiv.astro-ph/0102329,
title = {Generalized Fermi-Dirac Functions and Derivatives: Properties and Evaluation},
author = {Zhigang Gong and Ladislav Zejda and Werner Dappen and Josep M. Aparicio},
journal= {arXiv preprint arXiv:astro-ph/0102329},
year = {2009}
}
Comments
accepted for publication in Comp. Phys. Comm