Toward the Determination of Vietoris-like Polynomials

Abstract

This paper studies the relationship between polynomials and classical number sequences, focusing on their structural properties and mathematical significance. It explores a specific class of polynomials inspired by Vietoris' number sequences, referred to as Vietoris-like polynomials. The primary objective is to analyze their fundamental algebraic properties, recurrence relations, and special identities. The study employs algebraic methods to derive the recurrence relations and explicit formulas for these polynomials. Moreover, it establishes Catalan-like, Cassini-like, and d'Ocagne-like identities.

Keywords

• Polynomials
• Vietoris
• Vietoris-like polynomials

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