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
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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}, }