Uniform asymptotic approximation of Fermi-Dirac integrals (Q919736)
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scientific article; zbMATH DE number 4162135
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform asymptotic approximation of Fermi-Dirac integrals |
scientific article; zbMATH DE number 4162135 |
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Uniform asymptotic approximation of Fermi-Dirac integrals (English)
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1990
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The authors obtain an asymptotic expansion of the integral \(\frac{1}{\Gamma (q+1)}\int^{\infty}_{0}\frac{t^ qdt}{1+e^{t-x}}\) by an incomplete gamma function and elementary terms uniformly for large positive values of x and q. The result unifies four different cases considered earlier by \textit{H.-J. Schell} [Z. Anal. Anwend. 6, 421-438 (1987; Zbl 0638.41029)].
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Fermi-Dirac integrals
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saddle point method
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asymptotic expansion
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incomplete gamma function
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0.9267054
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0.9041361
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0.89744985
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0.8916307
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0.88362706
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0.88127893
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