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

Gil Gómez, Amparo; Odrzywolek, Andrzej; Segura Sala, José Javier; Temme, Nicolaas Maria

doi:10.1016/j.cpc.2022.108563

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Identificadores

URI: https://hdl.handle.net/10902/26903

DOI: 10.1016/j.cpc.2022.108563

ISSN: 0010-4655

Fecha

2023-02

Derechos

Attribution-NonCommercial-NoDerivatives 4.0 International

Publicado en

Computer Physics Communications, 2023, 283, 108563

Editorial

Elsevier

Enlace a la publicación

https://doi.org/10.1016/j.cpc.2022.108563

Palabras clave

Generalized Fermi-Dirac integral

Relativistic Fermi-Dirac integral

Asymptotic expansions

Numerical approximations

Matlab implementations

Resumen/Abstract

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.

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