Applications of Umbral Calculus Associated with p -Adic Invariant Integrals on Z p

Abstract

Recently, Dere and Simsek (2012) have studied the applications of umbral algebra to some special functions. In this paper, we investigate some properties of umbral calculus associated with $p$-adic invariant integrals on ${\mathbf{Z}}_p$. From our properties, we can also derive some interesting identities of Bernoulli polynomials.