Inequalities for gamma and q-gamma functions of complex arguments

被引：3
|
作者：
Ismail, Mourad E. H. [1 ,2 ]
机构：
[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
[2] King Saud Univ, Dept Math, Riyadh, Saudi Arabia
来源：
ANALYSIS AND APPLICATIONS | 2017年 / 15卷 / 05期
关键词：
Complete monotonicity; infinite divisibility; bounds; gamma function; q-gamma function; Lerch's inequality; MONOTONIC FUNCTIONS;
D O I：
10.1142/S0219530516500093
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the function Gamma(x + a)Gamma(x + b)/vertical bar Gamma(x + c + iy)vertical bar(2), a + b = 2c, and its q-analogue are of the form e-(h(x, y)) and h is completely monotonic in x. In particular both Gamma(x + a)Gamma(x + b)/vertical bar Gamma(x + c + iy)vertical bar(2) and Gamma(q)(x + a)Gamma(q) (x + b)/vertical bar Gamma(q)(x + c + iy)vertical bar(2) are Laplace transforms of infinitely divisible distributions. We also extend Lerch's inequality to the q-gamma function.
引用
收藏
页码：641 / 651
页数：11
相关论文
共 50 条
12345