Geometric polynomials via a differential operator

Abstract

In 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):

• 05A18
• 47E05
• 30C15

Key words:

• Geometric polynomials
• differential operator
• polynomials of real zeros
• Rolle’s theorem