A family of generalized q-Genocchi numbers and polynomials

TL;DR

This paper introduces a q-analogue extension of the generating function for higher-order generalized Genocchi numbers and polynomials associated with Dirichlet characters, expanding the mathematical framework of these special functions.

Contribution

It presents a novel q-extension of the generating function for generalized Genocchi numbers and polynomials linked to Dirichlet characters, broadening existing mathematical theories.

Findings

Derived new q-extensions for Genocchi numbers and polynomials

Connected the q-extensions to Dirichlet characters

Enhanced the theoretical understanding of special number sequences

Abstract

In this paper we consider the q-extension of the generating function for the higher-order generalized Genocchi numbers and polynomials attached to Dirichlet's character.