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Symmetry 2018, 10(12), 758; https://doi.org/10.3390/sym10120758

Some Generating Functions for q-Polynomials

1
Applied and Computational Mathematics Division, National Institute of Standards and Technology, Mission Viejo, CA 92694, USA
2
Departamento de Física y Matemáticas, Facultad de Ciencias, Universidad de Alcalá, Alcalá de Henares, 28871 Madrid, Spain
3
Department of Mathematics, University of Maryland, College Park, MD 20742, USA
*
Authors to whom correspondence should be addressed.
Received: 14 November 2018 / Revised: 30 November 2018 / Accepted: 13 December 2018 / Published: 16 December 2018
(This article belongs to the Special Issue Integral Transforms and Operational Calculus)
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Abstract

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. View Full-Text
Keywords: basic hypergeometric functions; generating functions; q-polynomials basic hypergeometric functions; generating functions; q-polynomials
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Cohl, H.S.; Costas-Santos, R.S.; Wakhare, T.V. Some Generating Functions for q-Polynomials. Symmetry 2018, 10, 758.

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