Umbral calculus associated with Bernoulli polynomials

TL;DR

This paper explores properties of umbral calculus related to Bernoulli polynomials, providing new identities and insights by building on recent work involving p-adic integrals and umbral techniques.

Contribution

It introduces novel properties of umbral calculus that facilitate deriving identities of Bernoulli polynomials, expanding theoretical understanding.

Findings

Derived new identities of Bernoulli polynomials

Connected umbral calculus with p-adic integrals

Enhanced theoretical framework for Bernoulli polynomial analysis

Abstract

Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These properties are useful in deriving some identities of Bernoulli polynomials.