Mohamed El Bachraoui, József Sándor
Published 2018-05-05Version 1
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.
Comments: Submitted 4 May 2018, pages 16
The Digamma function, Euler-Lehmer constants and their $p$-adic counterparts
Value-distribution of the Riemann zeta-function and related functions near the critical line
Some new inequalities for primes
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