%0 Journal Article
%T Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence coefficients
%A Lies Boelen
%A Walter Van Assche
%J Mathematics
%D 2013
%I arXiv
%R 10.1016/j.jat.2014.06.012
%X We look at some extensions of the Stieltjes-Wigert weight functions. First we replace the variable x by x^2 in a family of weight functions given by Askey in 1989 and we show that the recurrence coefficients of the corresponding orthogonal polynomials can be expressed in terms of a solution of the q-discrete Painlev\'e III equation. Next we consider the q-Laguerre or generalized Stieltjes-Wigert weight functions with a quadratic transformation and derive recursive equations for the recurrence coefficients of the orthogonal polynomials. These turn out to be related to the q-discrete Painlev\'e V equation. Finally we also consider the little q-Laguerre weight with a quadratic transformation and show that the recurrence coefficients of the orthogonal polynomials are again related to q-discrete Painlev\'e V.
%U http://arxiv.org/abs/1310.3960v2