Journal of Nonlinear Mathematical Physics

Volume 23, Issue 1, January 2016, Pages 1 - 20

Automorphisms of the q-deformed algebra suq(1, 1) and d-Orthogonal polynomials of q-Meixner type

Authors
Ali Zaghouani
Institut préparatoire aux études d'ingénieur de Bizerte, 7021 Bierte, Carthage university, Tunisia, ali.zaghouani12@hotmail.com
Received 23 May 2015, Accepted 31 August 2015, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2016.1135625How to use a DOI?
Keywords
d-orthogonal polynomials, q-deformed algebra suq(1, 1), q-coherent states, q-hypergeometric functions, q-Meixner polynomials, linear functional vector
Abstract

Starting from an operator given as a product of q-exponential functions in irreducible representations of the positive discrete series of the q-deformed algebra suq(1, 1), we express the associated matrix elements in terms of d-orthogonal polynomials. An algebraic setting allows to establish some properties : recurrence relation, generating function, lowering operator, explicit expression and d-orthogonality relations of the involved polynomials which are reduced to the orthogonal q-Meixner polynomials when d=1. If q ↑ 1, these polynomials tend to some d-orthogonal polynomials of Meixner type.

Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 1
Pages
1 - 20
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1135625How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Ali Zaghouani
PY  - 2021
DA  - 2021/01
TI  - Automorphisms of the q-deformed algebra suq(1, 1) and d-Orthogonal polynomials of q-Meixner type
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 20
VL  - 23
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1135625
DO  - https://doi.org/10.1080/14029251.2016.1135625
ID  - Zaghouani2021
ER  -