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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Bibliographic Details
Published in:Symmetry (Basel) Vol. 10; no. 12; p. 758
Main Authors: Cohl, Howard S., Costas-Santos, Roberto S., Wakhare, Tanay V.
Format: Journal Article
Language:English
Published: Switzerland MDPI AG 01.01.2018
Subjects:
Functions (mathematics)
Laplace transforms
Mathematical analysis
Polynomials
Radiation
q-polynomials
generating functions
33D45
basic hypergeometric functions
33C20
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary: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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Author Contributions: H.S.C., R.S.C.-S. and T.V.W. conceived the mathematics; H.S.C., R.S.C.-S. and T.V.W. wrote the paper.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym10120758