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

Ciccoli, Nicola; Koelink, Erik; Koornwinder, Tom H.

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

Authors

Ciccoli, Nicola

Koelink, Erik

Koornwinder, Tom H.

Description

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.
20 pages