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On Appell-Vietoris polynomials

Author(s): Cação, Isabel ; Falcão, M. I. ; Malonek, Helmuth R. ; Miranda, Fernando ; Tomaz, Graça

Date: 2024

Persistent ID: https://hdl.handle.net/1822/101374

Origin: RepositóriUM - Universidade do Minho

Project/scholarship: info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base/UIDB/00013/2020/PT; info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Programático/UIDP/00013/2020/PT; info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base/UIDB/04106/2020/PT; info:eu-repo/grantAgreement/FCT/Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Programático/UIDP/04106/2020/PT;

Subject(s): Appell polynomials; Combinatorial identities; Vietoris sequence

Description

In this paper we introduce a polynomial sequence (Vn(x))n≥0 involving the Vietoris’ number sequence and satisfying the Appell property. We derive several equivalent representations of Vn(x) and we deduce important relations closely related to the aforementioned Appell property. Finally, we address the problem of the zeros distribution of Vn(x) and conclude that, when n is even, the polynomials Vn(x) have no real zeros, whereas for odd n, the unique real zero of Vn(x) lies within the interval (-1,0).

Document Type Conference paper
Language English
Contributor(s) RepositóriUM - Universidade do Minho

Document details

On Appell-Vietoris polynomials

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