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Computation of the confluent hypergeometric function U(a, b, x) and its derivative for positive arguments

NUMERICAL ALGORITHMS (2023)

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

Amparo Gil et al.

Summary: This paper provides MATLAB implementations for approximations of the relativistic Fermi-Dirac integral and its partial derivatives. Numerical tests demonstrate that these expansions are efficient and accurate for a wide range of parameters. Therefore, our algorithms are expected to be valuable tools, together with other methods, for developing reliable and efficient software to compute these functions for all parameter ranges.

COMPUTER PHYSICS COMMUNICATIONS (2023)

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Article Mathematics

Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a, b and z

N. M. Temmea et al.

Summary: In this paper, new asymptotic expansions for the Kummer functions are proposed for large positive values of a, b, and z, with numerical tables provided to demonstrate the performance.

INDAGATIONES MATHEMATICAE-NEW SERIES (2022)

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Article Computer Science, Software Engineering