On the q-extension of higher-order Euler polynomials

TL;DR

This paper systematically studies generalized q-Euler numbers and polynomials of higher order, extending classical Euler concepts with q-analogs to explore their properties and relationships.

Contribution

It introduces a comprehensive framework for higher-order q-Euler polynomials and investigates their fundamental properties and potential applications.

Findings

Defined new families of q-Euler numbers and polynomials

Established key identities and recurrence relations

Explored connections with existing mathematical structures

Abstract

Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.