Sharp upper and lower bounds for the gamma function

被引：27
作者：
Alzer, Horst
机构：
[1] 51545 Waldbröl
来源：
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2009年 / 139卷
关键词：
D O I：
10.1017/S0308210508000644
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that fro all x > 0, we have root 2 pi x(x/e)(x) (x sinh 1/x)(x/2) (1 + alpha/x(5)) < Gamma(x + 1) < root 2 pi x(x/e)(x) (x sinh 1/x)(x/2) (1 + beta/x(5)) with the best possible constants alpha = 0 and beta = 1/1620.
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页码：709 / 718
页数：10
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