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
Descripción
Sumario: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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