A Harmonic Mean Inequality for the q-Gamma and q-Digamma Functions

被引：3

作者：

Bouali, Mohamed ^{[1
]}

机构：

[1] Fac Sci Tunis, Inst Preparatoire Etud Ingn Tunis, Campus Univ El Manar, El Manar Tunis 2092, Tunisia

来源：

FILOMAT | 2021年 / 35卷 / 12期

关键词：

q-Digamma function; q-Psi function; q-Gamma function; Gamma function; Digamma function; BOUNDS;

D O I：

10.2298/FIL2112105B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove among others results that the harmonic mean of Gamma(q)(x) and Gamma(q)(1/x) is greater than or equal to 1 for arbitrary x > 0, and q is an element of J where J is a subset of [0, +infinity). Also, we prove that there is a unique real number p(0) is an element of (1, 9/2), such that for q is an element of (0, p(0)), psi(q)(1) is the minimum of the harmonic mean of psi(q)(x) and psi(q)(1/x) for x > 0 and for q is an element of (p(0), +infinity), psi(q)(1) is the maximum. Our results generalize some known inequalities due to Alzer and Gautschi.

引用

页码：4105 / 4119

页数：15

共 25 条

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