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On a generalization of the Rogers generating function
Howard S. Cohl, Roberto S. Costas-Santos, Tanay Wakhare
We derive a generalized Rogers generating function and corresponding definite integral, for the continuous -ultraspherical polynomials by applying its connection relation and ut…
Some generating functions for q-polynomials
Howard S. Cohl, Roberto S. Costas-Santos, Tanay V. Wakhare
We obtain q-analogues of the Sylvester, Cesàro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.
Generalizations of generating functions for basic hypergeometric orthogonal polynomials
Howard S. Cohl, Roberto S. Costas-Santos, Philbert R. Hwang +1
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we gener…