Some Generating Functions for q-Polynomials

Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hyperge...

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Detalles Bibliográficos
Autores principales: Cohl, Howard S., Costas-Santos, Roberto S., Wakhare, Tanay V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9793654/
https://www.ncbi.nlm.nih.gov/pubmed/36578794
http://dx.doi.org/10.3390/sym10120758
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author Cohl, Howard S.
Costas-Santos, Roberto S.
Wakhare, Tanay V.
author_facet Cohl, Howard S.
Costas-Santos, Roberto S.
Wakhare, Tanay V.
author_sort Cohl, Howard S.
collection PubMed
description Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hypergeometric series (4)ϕ(5), (5)ϕ(5), (4)ϕ(3), (3)ϕ(2), (2)ϕ(1), and q-Pochhammer symbols. Starting with our q-generating functions, we are also able to find some new classical generating functions for the Pasternack and Bateman polynomials.
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spelling pubmed-97936542022-12-27 Some Generating Functions for q-Polynomials Cohl, Howard S. Costas-Santos, Roberto S. Wakhare, Tanay V. Symmetry (Basel) Article Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-generating functions are given in terms of the basic hypergeometric series (4)ϕ(5), (5)ϕ(5), (4)ϕ(3), (3)ϕ(2), (2)ϕ(1), and q-Pochhammer symbols. Starting with our q-generating functions, we are also able to find some new classical generating functions for the Pasternack and Bateman polynomials. 2018 /pmc/articles/PMC9793654/ /pubmed/36578794 http://dx.doi.org/10.3390/sym10120758 Text en https://creativecommons.org/licenses/by/4.0/This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Cohl, Howard S.
Costas-Santos, Roberto S.
Wakhare, Tanay V.
Some Generating Functions for q-Polynomials
title Some Generating Functions for q-Polynomials
title_full Some Generating Functions for q-Polynomials
title_fullStr Some Generating Functions for q-Polynomials
title_full_unstemmed Some Generating Functions for q-Polynomials
title_short Some Generating Functions for q-Polynomials
title_sort some generating functions for q-polynomials
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9793654/
https://www.ncbi.nlm.nih.gov/pubmed/36578794
http://dx.doi.org/10.3390/sym10120758
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