A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of
q-orthogonal polynomials containing the fundamental Askey–Wilson polynomials and their special cases. The function to be expanded
has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.
Keywords Basic hypergeometric functions -
q-orthogonal polynomials - Askey–Wilson polynomials - Continuous q-Jacobi polynomials - Continuous dual q-Hahn polynomials - Continuous q-ultraspherical polynomials - Al-Salam and Chihara polynomials - Continuous big q -Hermite polynomials - Continuous q-Hermite polynomials - Chebyshev polynomials - Jacobi polynomials
Mathematics Subject Classification (2000) 33D45 - 42C10 - 33D15