Research Article

Geometric polynomials via a differential operator

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 , 2024 , pages: 2247–2258

DOI: 10.2989/16073606.2024.2364306

Author(s): Said Taharbouchet University of M’hamed Bougra, Algeria , Miloud Mihoubi , Algeria

Keywords: 05A18 , 47E05 , 30C15 , Geometric polynomials , differential operator , polynomials of real zeros , Rolle’s theorem

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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.

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