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# Paper: Some generating functions for q-polynomials

## Some generating functions for q-polynomials

Cohl, H. S., Costas-Santos, R. S., and Wakhare, T. V. Symmetry-Basel 10, no. 12 (2018), 300—311

MDPI (SWITZERLAND) | ISSN: 2073-8994 | JCR® 2018 Impact Factor: 2.143 - MULTIDISCIPLINARY SCIENCES — position: 30/69 (Q2/T2)

## 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, 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},
}