A Study on Novel Extensions for the p -adic Gamma and p -adic Beta Functions

In this paper, we introduce the ρ , q -analog of the p-adic factorial function. By utilizing some properties of ρ , q -numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic ρ , q -gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2 . We also derive more representations of the p-adic ρ , q -gamma function in general case. Moreover, we consider the p-adic ρ , q -Euler constant derived from the derivation of p-adic ρ , q -gamma function at x = 1 . Furthermore, we provide a limit representation of aforementioned Euler constant based on ρ , q -numbers. Finally, we consider ρ , q -extension of the p-adic beta function via the p-adic ρ , q -gamma function and we then investigate various formulas and identities.

Abstract licence: CC BY

19 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.