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

Abstract

The g-Laguerre polynomials correspond to an indeterminate moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's i^i-summation, we complement the orthogonal g-Laguerre polynomials to 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 g-Jacobi polynomials. Interpretations on the SU(1,1) and 12(2) quantum groups are discussed.