A class of logarithmically completely monotonic functions and the best bounds in the second Kenshaw's double inequality

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:212

Article

Qi, Feng^1,2  Guo, Bai-Ni³ 

[1] Henan Univ, Coll Math & Informat Sci, Kaifeng City 475001, Henan Province, Peoples R China

[2] Henan Polytech Univ, Res Inst Math Inequal Theory, Jiaozuo City 454010, Henan Province, Peoples R China

[3] Henan Polytech Univ, Sch Math & Informat, Jiaozuo City 454010, Henan Province, Peoples R China

关键词: logarithmically completely monotonic function;    the second Kershaw's double inequality;    best bound;    gamma function;    psi function;    comparison;   

DOI  :  10.1016/j.cam.2006.12.022

来源: Elsevier

【 摘 要 】

In the article, the sufficient and necessary conditions such that a class of functions which involve the psi function Psi and the ratio Gamma(x + t)/Gamma(x + s) are logarithmically completely monotonic are established, the best bounds for the ratio Gamma(x + t)/Gamma(x + s) are given, and some comparisons with known results are carried out, where s and t are two real numbers and x > - min {s, t}. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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