Geometric polynomials via a differential operator

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.Mathematics Subject Classification (2020): 05A1847E0530C15Key words: Geometric polynomialsdifferential operatorpolynomials of real zerosRolle's theorem