A Unified Generating Function of the q-Genocchi Polynomials with their Interpolation Functions

TL;DR

This paper introduces a unified q-extension of Genocchi polynomials, explores their relations, and derives q-extensions of Hurwitz-zeta functions via Mellin transforms, enriching the mathematical framework of special functions.

Contribution

It constructs a unification q-extension of Genocchi polynomials and derives related Hurwitz-zeta type functions, providing new links between these mathematical objects.

Findings

Derived a unification q-extension of Genocchi polynomials

Established relations among the generalized polynomials

Obtained q-extensions of Hurwitz-zeta functions from Mellin transforms

Abstract

The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extensions of Hurwitz-zeta type functions from the Mellin transformation of this generating function which interpolates the unification of q-extension of Genocchi polynomials.