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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 Zp. From our properties, we can also derive some interesting identities of Bernoulli polynomials

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Applications of Umbral Calculus Associated with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-Adic Invariant Integrals on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="bold">Z</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>

Applications of Umbral Calculus Associated withp-Adic Invariant Integrals onZp