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

Access to Document

10.1016/j.indag.2015.04.004

Cite this

@article{1426ef8deb6443e69f338984b65a3ba2,

title = "On q-deformed generalized Touchard polynomials",

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.",

keywords = "Generalized Stirling numbers, Spivey relation, Touchard polynomials, q-deformation",

author = "Toufik Mansour and Matthias Schork",

note = "Publisher Copyright: {\textcopyright} 2015 Royal Dutch Mathematical Society (KWG).",

year = "2015",

month = aug,

day = "1",

doi = "10.1016/j.indag.2015.04.004",

language = "English",

volume = "26",

pages = "634--645",

journal = "Indagationes Mathematicae",

issn = "0019-3577",

publisher = "Elsevier",

number = "4",

}

TY - JOUR

T1 - On q-deformed generalized Touchard polynomials

AU - Mansour, Toufik

AU - Schork, Matthias

PY - 2015/8/1

Y1 - 2015/8/1

N2 - 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.

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 - http://www.scopus.com/inward/record.url?scp=84937813553&partnerID=8YFLogxK

U2 - 10.1016/j.indag.2015.04.004

DO - 10.1016/j.indag.2015.04.004

M3 - Article

AN - SCOPUS:84937813553

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

Other files and links

Fingerprint

Cite this