A new class of generalized Genocchi polynomials

TL;DR

This paper introduces a novel class of generalized Genocchi polynomials utilizing q-integers, deriving q-analogues of classical formulas and an addition theorem, expanding the mathematical framework of these polynomials.

Contribution

It presents a new class of generalized Genocchi polynomials based on q-integers and derives their key q-analogues and addition theorem, advancing the theoretical understanding.

Findings

Derived q-analogues of classical formulas

Established a q-analogue of the Srivastava--Pintér addition theorem

Expanded the theoretical framework of Genocchi polynomials

Abstract

The main purpose of this paper is to introduce and investigate a new class of generalized Genocchi polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava--Pint\'er addition theorem is obtained.