Complete asymptotic expansions for the relativistic Fermi-Dirac integral
A. Gil, J. Segura, N. M. Temme
TL;DR
This paper derives new complete asymptotic expansions for the relativistic Fermi-Dirac integral, aiding in understanding Fermi systems across various physical contexts.
Contribution
It provides novel and comprehensive asymptotic expansions for the relativistic Fermi-Dirac integral, improving analytical tools for related physical problems.
Findings
Expansions are accurate and complete for various regimes.
Numerical examples demonstrate the effectiveness of the expansions.
The results facilitate better qualitative understanding of Fermi systems.
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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Taxonomy
TopicsMathematical functions and polynomials · Spectral Theory in Mathematical Physics · Electromagnetic Scattering and Analysis