Logarithmically completely monotonic functions related to the q-gamma function and its applications

被引：8

作者：

Mehrez, Khaled ^{[1
]}

Das, Sourav ^{[2
]}

机构：

[1] Univ Kairouan, Kairouan Preparatory Inst Engn Studies, Dept Math, Kairouan 3100, Tunisia

[2] Natl Inst Technol Jamshedpur, Dept Math, Jamshedpur 831014, Jharkhand, India

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 02期

关键词：

q-digamma function; q-gamma function; Completely monotonic function; Logarithmically completely monotonic function; Inequalities; Q-DIGAMMA; TRIGAMMA;

D O I：

10.1007/s13324-022-00678-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our main goal in this paper is to introduce new classes of logarithmically completely monotonic functions involving q-gamma function. As applications, new classes of Bernstein functions related to the q-gamma function and dilogarithm are established with its integral representation. Moreover, various new sharp bounds for the q-digamma and q-trigamma functions are derived. In particular, sharp bounds for the q-analogue of harmonic numbers are established as a consequence. The results obtained in this work are new. The limiting case q -> 1, in the results obtained in this paper leads to the results for a class of Bernstein functions and logarithmically completely monotonic function involving Euler's gamma function and dilogarithm, which are also new in the literature.

引用

页数：20

共 29 条

[1] Sharp inequalities for the digamma and polygamma functions [J].