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q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations

Nicola Ciccoli·Erik Koelink·Tom H. Koornwinder
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Abstract

The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's ${}_1ψ_1$-summation we complement the orthogonal q-Laguerre polynomials into an explicit orthogonal basis for the corresponding L^2-space. The dual orthogonal system consists of so-called big q-Bessel functions, which can be obtained as a rigorous limit of the orthogonal system of big q-Jacobi polynomials. Interpretations on the SU(1,1) and E(2) quantum groups are discussed.

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Nicola Ciccoli, Erik Koelink, Tom H. Koornwinder. 1998-05-06. q-Laguerre polynomials and big q-Bessel functions and their orthogonality relations. https://arxiv.org/abs/math/9805023

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