The fermionic p-adic integrals on Zp associated with extended q-Euler numbers and polynomials

TL;DR

This paper explores the properties of q-Euler numbers and polynomials using fermionic p-adic integrals, revealing new q-analogues of Stirling number identities.

Contribution

It introduces a systematic approach to studying higher-order q-Euler numbers and polynomials via multivariate fermionic p-adic integrals on Zp, extending existing mathematical frameworks.

Findings

Derived new identities for q-Euler numbers and polynomials

Established q-analogues of Stirling number identities

Provided a comprehensive analysis of multivariate fermionic p-adic integrals

Abstract

The purpose of this paper is to present a systemic study of some families of q-Euler numbers and polynomials of Norlund's type by using multivariate fermionic p-adic integral on Zp. Moreover, the study of these higher-order q-Euler numbers and polynomials implies some interesting q-analogue of stirling numbers identities.