A harmonic mean inequality for the $q-$gamma and $q-$digamma functions

Mohamed Bouali

We prove amongs 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 $q\in J$ where $J$ is a subset of $[0,+\i…