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arXiv · 1803.09636

Dual addition formulas: the case of continuous $q$-ultraspherical and $q$-Hermite polynomials

Tom H. Koornwinder
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Abstract

We settle the dual addition formula for continuous $q$-ultraspherical polynomials as an expansion in terms of special $q$-Racah polynomials for which the constant term is given by the linearization formula for the continuous $q$-ultraspherical polynomials. In a second proof we derive the dual addition formula from the Rahman--Verma addition formula for these polynomials by using the self-duality of the polynomials. We also consider the limit case of continuous $q$-Hermite polynomials.

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Tom H. Koornwinder. 2018-03-26. Dual addition formulas: the case of continuous $q$-ultraspherical and $q$-Hermite polynomials. https://doi.org/10.1007/s11139-021-00426-7

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