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arXiv · 1805.01999

Some new inequalities for the $q$-gamma and related functions

Mohamed El Bachraoui·József Sándor
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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 $\psi_q(x)$, and the $q$-series. Among other consequences, we improve a result of Azler~and~Grinshpan about the zeros of the function $\psi_q(x)$. We use $q$-analogues for the Gauss multiplication formula to put in closed form members of some of our inequalities.

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Mohamed El Bachraoui, József Sándor. 2018-05-05. Some new inequalities for the $q$-gamma and related functions. https://arxiv.org/abs/1805.01999

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