Recording date: 01/09/2011
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On generalized Stieltjes - Wigert polynomials

The generalized Stieltjes{Wigert polynomials depending on parameters 0  p < 1 and 0 < q < 1 are
discussed. By removing the mass at zero of the N-extremal solution concentrated in the zeros of the
D-function from the Nevanlinna parametrization, we obtain a discrete measure mM which is uniquely
determined by its moments. We calculate the coecients of the corresponding orthonormal polynomials
(PM
n ). As noticed by T. Chihara, these polynomials are the shell polynomials corresponding to the maximal
parameter sequence for a certain chain sequence. We also nd the minimal parameter sequence, as well as
the parameter sequence corresponding to the generalized Stieltjes{Wigert polynomials, and compute the
value of related continued fractions. The mass points of mM have been studied in recent papers of Hayman,
Ismail{Zhang and Huber. In the special case of p = q, the maximal parameter sequence is constant and
the determination of mM and (PM
n ) gives an answer to a question posed by T. Chihara in 2001.
** This is a joint work with: Jacob S. Christiansen

Chistian Berg
Chistian Berg