On the real-rootedness of generalized Touchard polynomials

Chak On Chow; Toufik Mansour

doi:10.1016/j.amc.2014.12.108

On the real-rootedness of generalized Touchard polynomials

Chak On Chow, Toufik Mansour

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the real-rootedness of generalized Touchard polynomials recently revisited by Mansour and Schork (2013). Towards this end, we first describe the normal form of the generalized Touchard polynomials, by which recurrence relations for the polynomial part are derived. By using the recurrence relations, we prove the real-rootedness of the generalized Touchard polynomials for the parameter m ∈ [1, ∞)∪ {k/k+1 : k ∈ ℕ}.

Original language	English
Pages (from-to)	204-209
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	254
DOIs	https://doi.org/10.1016/j.amc.2014.12.108
State	Published - 1 Mar 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc. All rights reserved.

Keywords

Alternating
Generalized touchard polynomials
Interlacing
Real-rootedness

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.12.108

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abstract = "We consider the real-rootedness of generalized Touchard polynomials recently revisited by Mansour and Schork (2013). Towards this end, we first describe the normal form of the generalized Touchard polynomials, by which recurrence relations for the polynomial part are derived. By using the recurrence relations, we prove the real-rootedness of the generalized Touchard polynomials for the parameter m ∈ [1, ∞)∪ {k/k+1 : k ∈ ℕ}.",

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AB - We consider the real-rootedness of generalized Touchard polynomials recently revisited by Mansour and Schork (2013). Towards this end, we first describe the normal form of the generalized Touchard polynomials, by which recurrence relations for the polynomial part are derived. By using the recurrence relations, we prove the real-rootedness of the generalized Touchard polynomials for the parameter m ∈ [1, ∞)∪ {k/k+1 : k ∈ ℕ}.

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KW - Generalized touchard polynomials

KW - Interlacing

KW - Real-rootedness

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On the real-rootedness of generalized Touchard polynomials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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