Grunbaum-Type Inequalities for Gamma and Incomplete Gamma Functions

被引：0
|
作者：
Alzer, Horst [1 ]
Kwong, Man Kam [2 ]
机构：
[1] Morsbacher Str 10, D-51545 Waldbrol, Germany
[2] Hong Kong Polytech Univ, Dept Appl Math, Hunghom, Hong Kong, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2018年 / 73卷 / 04期
关键词：
Gamma function; incomplete gamma functions; Grunbaum-type inequalities; Euler's constant;
D O I：
10.1007/s00025-018-0913-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that the gamma and incomplete gamma functions satisfy certain functional inequalities of Grunbaum-type. Among our results is a new characterization of Euler's constant C, namely, it is the smallest real number such that the inequality 1/(1+x)(C)Gamma(1+x) + 1/(1+y)(C)Gamma(1+y) <= 1 + 1/(1+z)(C)Gamma(1+z) holds for all x, y, z >= 0 with x(2) + y(2) = z(2).
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页数：7
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