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

1998/05/06 by Nicola Ciccoli, Erik Koelink, Tom H. Koornwinder
Mathematics · #math.CA #math.QA #msc:33D45 #msc:33D80

paper · pdf

published as Methods Appl. Anal. 6 (1999), 109-127 · 20 pages

arxiv created 1998/05/06 · arxiv updated 2009/11/30

Abstract

The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's ₁ψ₁-summation we complement the orthogonal q-Laguerre polynomials into an explicit orthogonal basis for the corresponding L²-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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