Some generating functions for q-polynomials
Cohl, H. S., Costas-Santos, R. S., and Wakhare, T. V. Symmetry-Basel 10, no. 12 (2018), 758, 300—311Abstract
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
Link | Size | Description |
---|---|---|
paper_20.pdf | 303 KB | Preprint (PDF, 18 Pages, 5 Tables) |
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}, }