Howard S. Cohl, Roberto S. Costas-Santos, Philbert R. Hwang
Published 2014-11-05Version 1
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for Askey-Wilson, Rogers/continuous $q$-ultrapherical, little $q$-Laguerre/Wall, and $q$-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and $q$-integrals.
Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals
Some classes of generating functions for generalized Hermite- and Chebyshev-type polynomials: Analysis of Euler's formula
Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme
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