Summary
Some simple ideas are used here to prove a theorem on generating functions for a certain class of q-polynomials. This general theorem is then applied to derive a fairly large number of known as well as new generating functions for the familiar q-analogues of various polynomial systems including, for example, the classical orthogonal polynomials of Hermite, Jacobi, and Laguerre. A number of other interesting consequences of the theorem are also discussed.
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Srivastava, H.M., Agarwal, A.K. Generating functions for a class ofq-polynomials. Annali di Matematica pura ed applicata 154, 99–109 (1989). https://doi.org/10.1007/BF01790345
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DOI: https://doi.org/10.1007/BF01790345