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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials


Authors: Lies Boelen and Walter Van Assche
Journal: Proc. Amer. Math. Soc. 138 (2010), 1317-1331
MSC (2010): Primary 39A13, 33C45; Secondary 42C05
Published electronically: December 8, 2009
MathSciNet review: 2578525
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Abstract: We consider two semiclassical extensions of the Laguerre weight and their associated sets of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy discrete Painlevé equations.


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Additional Information

Lies Boelen
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, BE-3001 Leuven, Belgium
Email: lies.boelen@wis.kuleuven.be

Walter Van Assche
Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, BE-3001 Leuven, Belgium
Email: walter@wis.kuleuven.be

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10152-1
PII: S 0002-9939(09)10152-1
Keywords: Discrete Painlev\'e equations, orthogonal polynomials
Received by editor(s): February 23, 2009
Received by editor(s) in revised form: July 2, 2009
Published electronically: December 8, 2009
Additional Notes: This research was supported by K. U. Leuven Research Grant OT/08/033, FWO Research Grant G.0427.09 and the Belgian Interuniversity Attraction Poles Programme P6/02.
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.