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

The q-Laguerre polynomials correspond to an indeterminate moment problem. For explicit discrete non-N-extremal measures corresponding to Ra- manujan’s 1ψ1-summation, we complement the orthogonal q-Laguerre polyno- mials to an explicit orthogonal basis for the corresponding L2-space. The dual orthogonal system consists of so-called big q-Bessel functions, which can be ob- tained 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.