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

Download

BibTeX

@article {Cohletall2018,
AUTHOR = {Cohl, Howard S., Costas-Santos, Roberto S. and Wakhare, Tanay},
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},
}