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AbstractIn this paper, we use differential operator to present new identities and provide alternative proofs for certain established identities related to geometric polynomials. Additionally, by using the differential operator associated with geometric polynomials, Rolle’s theorem and a theorem of Wang and Yeh, we present some results on the real rootedness of polynomials. [ABSTRACT FROM AUTHOR]

In this paper, by the classical umbral calculus method, we establish identities involving the Appell polynomials and extend some existing identities. [ABSTRACT FROM AUTHOR]

In this paper we give some congruences on the r-derangement polynomials (defined below), Lah polynomials and some versions of Bell numbers and polynomials. [ABSTRACT FROM AUTHOR]