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

University of Haifa

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	American 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

Keywords

Alternating
Generalized touchard polynomials
Interlacing
Real-rootedness

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2014.12.108

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title = "On the real-rootedness of generalized Touchard polynomials",

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\}.",

keywords = "Alternating, Generalized touchard polynomials, Interlacing, Real-rootedness",

author = "Chow, \{Chak On\} and Toufik Mansour",

year = "2015",

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doi = "10.1016/j.amc.2014.12.108",

language = "American English",

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journal = "Applied Mathematics and Computation",

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AU - Mansour, Toufik

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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}.

KW - Alternating

KW - Generalized touchard polynomials

KW - Interlacing

KW - Real-rootedness

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DO - 10.1016/j.amc.2014.12.108

M3 - Article

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VL - 254

SP - 204

EP - 209

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On the real-rootedness of generalized Touchard polynomials

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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