The indeterminate moment problem for the image-Meixner polynomials Original Research Article

For a class of orthogonal polynomials related to the qq-Meixner polynomials corresponding to an indeterminate moment problem we give a one-parameter family of orthogonality measures. For these measures we complement the orthogonal polynomials to an orthogonal basis for the corresponding weighted L2L2-space explicitly. The result is proved in two ways; by a spectral decomposition of a suitable operator and by direct series manipulation. We discuss extensions to explicit non-positive measures and the relation to other indeterminate moment problems for the continuous dual q−1q−1-Hahn and qq-Laguerre polynomials.