Evaluation of the generalized Fermi-Dirac integral and its derivatives for moderate/large values of the parameters

Approximations with Matlab implementations for the relativistic Fermi-Dirac integral and its partial derivatives are given in this paper. As the numerical tests show, the expansions allow to calculate the functions efficiently and with high accuracy for a large range of parameters. Therefore, our algorithms are expected to be a very useful tool, in combination with other methods, for building reliable and efficient software for computing the functions for all the parameters ranges. Program Title: FermiDiracExpans CPC Library link to program files: https://doi.org/10.17632/sk34wtcxhh.1 Licensing provisions: GPLv3 Programming language: Matlab Nature of problem: The evaluation of the relativistic Fermi-Dirac function and its partial derivatives is needed in different problems in applied and theoretical physics, such as stellar astrophysics, plasma physics or electronics. Solution method: Convergent and asymptotic expansions are provided to approximate the relativistic Fermi-Dirac function and its derivatives for moderate/large values of its parameters. Additional comments including restrictions and unusual features: The functions work in recent versions of Matlab (from version R2014b on).