q Analogue of p adic log gamma functions associated with modified q extension of Genocchi numbers with weight alpha and beta

TL;DR

This paper introduces a q-analogue of p-adic log gamma functions with weights alpha and beta, exploring their relationships with q-extensions of Genocchi and modified q Euler numbers, advancing the understanding of q-analogue functions.

Contribution

It presents a new q-analogue of p-adic log gamma functions with weights, establishing connections with q-extensions of Genocchi and Euler numbers, which is a novel theoretical development.

Findings

Defined q-analogue of p-adic log gamma functions with weights.

Established relationships with q-extensions of Genocchi and Euler numbers.

Provided theoretical formulas and properties of these functions.

Abstract

The fundamental aim of this paper is to describe q-Analogue of p-adic log gamma functions with weight alpha and beta. Moreover, we give relationship between p-adic q-log gamma funtions with weight ({\alpha}, {\beta}) and q-extension of Genocchi numbers with weight alpha and beta and modified q Euler numbers with weight {\alpha}