Extended Fermionic p-Adic q-Integrals On Zp In Connection With Applications Of Umbral Calculus

TL;DR

This paper explores the use of extended fermionic p-adic q-integrals on Zp to derive new properties of Euler numbers and polynomials, connecting umbral calculus with Sheffer sequences.

Contribution

It introduces novel applications of umbral calculus via p-adic q-integrals, revealing new properties of Euler numbers and polynomials and their generating functions.

Findings

New properties of Euler numbers and polynomials derived

Connection established between Sheffer sequences and weighted Euler polynomials

Systematic study of generating functions for Euler-related sequences

Abstract

The purpose of this paper is to derive some applications of umbral calculus by using extended fermionic p-adic q-integral on Zp. From those applications, we derive some new interesting properties on the new family of Euler numbers and polynomials. That is, a systemic study of the class of Sheffer sequences in connection with generating function of the weighted Euler polynomials are given in the present paper.