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Some generating functions for $$q$$-polynomials. (English) Zbl 1425.33009
Summary: 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.
##### MSC:
 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33C20 Generalized hypergeometric series, $${}_pF_q$$
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##### References:
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