UNIFORM ASYMPTOTIC APPROXIMATION OF FERMI-DIRAC INTEGRALS

被引：7

作者：

TEMME, NM ^{[1
]}

OLDEDAALHUIS, AB ^{[1
]}

机构：

[1] CTR MATH & COMP SCI, 1009 AB AMSTERDAM, NETHERLANDS

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1990年 / 31卷 / 03期

关键词：

error function; incomplete gamma function; saddle point method; Uniform asymptotic expansions of integrals;

D O I：

10.1016/0377-0427(90)90038-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Fermi-Dirac integral Fq(x)= 1 Γ(q+1) ∫ 0 ∞ tq 1+et-xdt, q>-1, is considered for large positive values of x and q. The results are obtained from a contour integral in the complex plane. The approximation contains a finite sum of simple terms, an incomplete gamma function and an infinite asymptotic series. As follows from earlier results, the incomplete gamma function can be approximated in terms of an error function. © 1990.

引用

页码：383 / 387

页数：5

共 8 条

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[7] ASYMPTOTIC-EXPANSION OF THE INCOMPLETE GAMMA-FUNCTIONS
TEMME, NM
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1979, 10 (04) : 757 - 766
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