Complete monotonicity involving some ratios of gamma functions

Journal of inequalities and applications

Zhen-Hang Yang¹ 

关键词: completely monotonic function;    logarithmically completely monotonic function;    gamma function;    psi function;    33B15;    33B10;    26A48;   

DOI  :  10.1186/s13660-017-1527-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and logarithmically completely monotonic. As consequences, these not only unify and improve certain known results including Qi’s and Ismail’s conclusions, but also can generate some new inequalities.

【 授权许可】

CC BY