Improving Stirling's formula

被引：0

作者：

Batir, Necdet ^{[1
]}

机构：

[1] Nevsehir Univ, Fac Arts & Sci, Dept Math, Nevsehir, Turkey

来源：

MATHEMATICAL COMMUNICATIONS | 2011年 / 16卷 / 01期

关键词：

Stirling formula; Burnside's formula; gamma function; digamma function; inequalities; GAMMA-FUNCTIONS; APPROXIMATIONS; INEQUALITIES; SERIES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We calculated the optimal values of the real parameters a and b in such a way that the asymptotic formula n ! similar to e(-a) (n+a/e)(n) root 2 pi(n+b) (as n -> infinity) gives the best accurate values for n !. Our estimations improve the classical Stirling and Burnside's formulas and their several recent improvements due to the author and C. Mortici. Apart from their simplicities and beauties our formulas give very accurate values for factorial n. Also, our results lead to new upper and lower bounds for the gamma function and recover some published inequalities for the gamma function.

引用

页码：105 / 114

页数：10

共 18 条

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