On q-deformed generalized Touchard polynomials

Toufik Mansour; Matthias Schork

doi:10.1016/j.indag.2015.04.004

On q-deformed generalized Touchard polynomials

Toufik Mansour
, Matthias Schork

Department of Mathematics

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

Abstract

A q-deformed analog of the generalized Touchard polynomials is considered and the connection to generalized Stirling numbers and Bell polynomials is established. For low order m, the q-deformed generalized Touchard polynomials are shown to be related to q-deformed exponential polynomials (m = 1), q-deformed Laguerre polynomials (m = 2), and q-deformed Bessel polynomials (m = - 1). A recurrence relation for the q-deformed generalized Touchard polynomials is derived, representing a generalization of Spivey's relation.

Original language	English
Pages (from-to)	634-645
Number of pages	12
Journal	Indagationes Mathematicae
Volume	26
Issue number	4
DOIs	https://doi.org/10.1016/j.indag.2015.04.004
State	Published - 1 Aug 2015

Bibliographical note

Publisher Copyright:
© 2015 Royal Dutch Mathematical Society (KWG).

Keywords

Generalized Stirling numbers
Spivey relation
Touchard polynomials
q-deformation

ASJC Scopus subject areas

General Mathematics

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10.1016/j.indag.2015.04.004

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AU - Schork, Matthias

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AB - A q-deformed analog of the generalized Touchard polynomials is considered and the connection to generalized Stirling numbers and Bell polynomials is established. For low order m, the q-deformed generalized Touchard polynomials are shown to be related to q-deformed exponential polynomials (m = 1), q-deformed Laguerre polynomials (m = 2), and q-deformed Bessel polynomials (m = - 1). A recurrence relation for the q-deformed generalized Touchard polynomials is derived, representing a generalization of Spivey's relation.

KW - Generalized Stirling numbers

KW - Spivey relation

KW - Touchard polynomials

KW - q-deformation

UR - https://www.scopus.com/pages/publications/84937813553

U2 - 10.1016/j.indag.2015.04.004

DO - 10.1016/j.indag.2015.04.004

M3 - Article

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SN - 0019-3577

VL - 26

SP - 634

EP - 645

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 4

ER -

On q-deformed generalized Touchard polynomials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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