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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Computer Physics Communications
Scientific Computing

Gil, A., Odrzywolek, A., Segura, J., & Temme, N. (2023). Evaluation of the generalized Fermi-Dirac integral and its derivatives for moderate/large values of the parameters. Computer Physics Communications, 283, 108563:1–108563:9. doi:10.1016/j.cpc.2022.108563