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

 

Rodrigues type formula for orthogonal polynomials on the unit ball


Author: Yuan Xu
Journal: Proc. Amer. Math. Soc. 133 (2005), 1965-1976
MSC (2000): Primary 33C50, 42C10
Published electronically: February 24, 2005
MathSciNet review: 2137862
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Abstract: For a class of weight functions invariant under reflection groups on the unit ball, a family of orthogonal polynomials is defined via a Rodrigues type formula using the Dunkl operators. Their properties and their relation with several other bases are explored.


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Additional Information

Yuan Xu
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
Email: yuan@math.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07885-8
PII: S 0002-9939(05)07885-8
Keywords: Orthogonal polynomials on a unit ball, Rodrigues type formula, biorthogonal polynomials, reflection invariant weight function
Received by editor(s): February 13, 2003
Published electronically: February 24, 2005
Additional Notes: This work was partially supported by the National Science Foundation under Grant DMS-0201669
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society