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Title: Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence coefficients
Authors: Boelen, Lies ×
Van Assche, Walter #
Issue Date: May-2015
Publisher: Academic Press
Series Title: Journal of Approximation Theory vol:193 pages:56-73
Abstract: 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 Painlevé 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 Painlevé 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-Painlevé V.
ISSN: 0021-9045
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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