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Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials
Author(s):
Lies
Boelen;
Walter
Van Assche
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1317-1331.
MSC (2010):
Primary 39A13, 33C45;
Secondary 42C05
Posted:
December 8, 2009
MathSciNet review:
2578525
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Additional information
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:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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