Paper: Some generating functions for q-polynomials

Some generating functions for q-polynomials

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 \({}_4\phi_5\), \({}_5\phi_5\) \({}_4\phi_3\), \({}_3\phi_2\), \({}_2\phi_1\) 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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BibTeX

@article {Cohletall2018,
AUTHOR={Cohl, H. S., Costas-Santos, Roberto S. and Wakhare, T. V.},
TITLE={Some generating functions for $q$-polynomials},
JOURNAL={Symmetry},
FJOURNAL={Symmetry},
VOLUME={10},
YEAR={2018},
NUMBER={12},
PAGES={758, 12 pages},
ISSN={2073-8994},
DOI={10.3390/sym10120758},
URL={https://doi.org/10.3390/sym10120758},
}