Logarithmically complete monotonicity of ratios of q-gamma functions

被引：8
|
作者：
Tian, Jing-Feng [1 ]
Yang, Zhenhang [2 ]
机构：
[1] North China Elect Power Univ, Dept Math & Phys, Yonghua St 619, Baoding 071003, Peoples R China
[2] Zhejiang Elect Power Soc, Hangzhou 310008, Zhejiang, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 508卷 / 01期
关键词：
q-psi function; Logarithmically complete; monotonicity; Complete monotonicity; INEQUALITIES; BOUNDS;
D O I：
10.1016/j.jmaa.2021.125868
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For u, v, r, s is an element of R and 0 < q not equal 1, let Gamma(q) , psi(q) be the q-gamma,-psi functions and let W-q;u,W-v be defined on (- min {u, v} , infinity) by W-q;u,W-v (x) =(Gamma(q) (x + u)/Gamma(q)(x + v))(1/(u - v)) = if u not equal v and W-q;u,W-u (x) = e(psi q(x+u).) In this paper, by a new way we present the necessary and sufficient conditions for the ratio (W-q;u,W-v/W-q;r,W-s) to be logarithmically completely monotonic on (-rho, infinity), where rho = min {u, v, r, s}. This extends and generalizes some existing results. (c) 2021 Elsevier Inc. All rights reserved.
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页数：13
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