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Complete asymptotic expansions for the relativistic Fermi-Dirac integral

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arxiv 2108.11210 v2 pith:CQQWBRVC submitted 2021-08-25 math.CA

A. Gil , J. Segura , N. M. Temme This is my paper · ORCID
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keywords expansionsfermi-diracasymptoticcompleteintegralrelativisticappearapplication
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Fermi-Dirac integrals appear in problems in nuclear astrophysics, solid state physics or in the fundamental theory of semiconductor modeling, among others areas of application. In this paper, we give new and complete asymptotic expansions for the relativistic Fermi-Dirac integral. These expansions could be useful to obtain a correct qualitative understanding of Fermi systems. The performance of the expansions is illustrated with numerical examples.

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  1. Diophantine FLINT-HILLS series

    math.GM 2025-01 reject novelty 4.0 of 10

    The paper claims a proof of convergence of the Flint-Hills series and a new irrationality-measure bound mu(pi) <= 2.5, but the proof is circular and invalid.

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