A FUNCTIONAL INEQUALITY FOR THE GAMMA FUNCTION

被引：0
|
作者：
Alzer, Horst
机构：
[1] Morsbacher Str. 10
来源：
ANALYSIS AND APPLICATIONS | 2013年 / 11卷 / 02期
关键词：
Gamma function; functional inequality; Euler's constant;
D O I：
10.1142/S0219530513500103
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let alpha and beta be real numbers. We prove that the functional inequality Gamma(x)Gamma(y) <= Gamma(x Gamma G(y)(alpha) + y Gamma(x)(beta)) holds for all positive real numbers x and y if and only if alpha = beta = 1/gamma(1 - gamma) = 4.09772 ... Here, gamma denotes Euler's constant.
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页数：11
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