The moment problem associated with the Stieltjes–Wigert polynomials

We consider the indeterminate Stieltjes moment problem associated with the Stieltjes–Wigert polynomials. After a presentation of the well-known solutions, we study a transformation T of the set of solutions. All the classical solutions turn out to be fixed under this transformation but this is not the case for the so-called canonical solutions. Based on generating functions for the Stieltjes– Wigert polynomials, expressions for the entire functions A, B, C, and D from the Nevanlinna parametrization are obtained.We describe T (n)(μ) for n ∈ N when μ = μ0 is a particular N-extremal solution and explain in detail what happens when n→∞.  2002 Elsevier Science (USA). All rights reserved