Stieltjes–Wigert polynomials
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Not to be confused with Stieltjes polynomial.
For the generalized Stieltjes–Wigert polynomials, see q-Laguerre polynomials.
In mathematics, Stieltjes–Wigert polynomials (named after Thomas Jan Stieltjes and Carl Severin Wigert) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function [1]
on the positive real line x > 0.
The moment problem for the Stieltjes–Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials (see Krein's condition).
Koekoek et al. (2010) give in Section 14.27 a detailed list of the properties of these polynomials.