Some Properties of the q -Extension of the p -Adic Gamma Function

Abstract

We study the $q$-extension of the $p$-adic gamma function ${\mathrm{\Gamma }}_{p,q}$. We give a new identity for the $q$-extension of the $p$-adic gamma ${\mathrm{\Gamma }}_{p,q}$ in the case $p=2$. Also, we derive some properties and new representations of the $q$-extension of the $p$-adic gamma ${\mathrm{\Gamma }}_{p,q}$ in general case.