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.
Complete asymptotic expansions for the relativistic Fermi-Dirac integral
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abstract
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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math.GM 1years
2025 1verdicts
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Diophantine FLINT-HILLS series
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.