Some new inequalities for the q-gamma and related functions

2018/05/05 by Mohamed El Bachraoui, Bachraoui, Mohamed El, József Sándor +1
Mathematics · #26D15 #33B15 #33E05 #Advanced Mathematical Identities #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1805.01999

openalex publication_date 2018/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider convexity and monotonicity properties for some functions related to the q-gamma function. As applications, we give a variety of inequalities for the q-gamma function, the q-digamma function ψ_q(x), and the q-series. Among other consequences, we improve a result of Azler~and~Grinshpan about the zeros of the function ψ_q(x). We use q-analogues for the Gauss multiplication formula to put in closed form members of some of our inequalities.

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