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Zbl 0707.65008
Temme, N.M.; Olde Daalhuis, A.B.
(Daalhuis, A.B.Olde)
Uniform asymptotic approximation of Fermi-Dirac integrals. (English)
[J] J. Comput. Appl. Math. 31, No.3, 383-387 (1990). ISSN 0377-0427

The authors obtain an asymptotic expansion of the integral $\frac{1}{\Gamma (q+1)}\int\sp{\infty}\sb{0}\frac{t\sp qdt}{1+e\sp{t-x}}$ 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 {\it H.-J. Schell} [Z. Anal. Anwend. 6, 421-438 (1987; Zbl 0638.41029)].
[L.Berg]

MSC 2000:: *65D20 Computation of special functions
41A60 Asymptotic problems in approximation
33B20 Incomplete beta and gamma functions

Keywords: Fermi-Dirac integrals; saddle point method; asymptotic expansion; incomplete gamma function

Citations: Zbl 0638.41029

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