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Explicit orthogonal polynomials for reciprocal polynomial weights on $ (-\infty ,\infty )$


Author: D. S. Lubinsky
Journal: Proc. Amer. Math. Soc. 137 (2009), 2317-2327
MSC (2000): Primary 42C05
Published electronically: December 18, 2008
MathSciNet review: 2495265
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Abstract: Let $ S$ be a polynomial of degree $ 2n+2$, that is, positive on the real axis, and let $ w=1/S$ on $ (-\infty ,\infty )$. We present an explicit formula for the $ n$th orthogonal polynomial and related quantities for the weight $ w$. This is an analogue for the real line of the classical Bernstein-Szegő formula for $ \left(-1,1\right)$.


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Additional Information

D. S. Lubinsky
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: lubinsky@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09754-2
Keywords: Orthogonal polynomials, Bernstein-Szeg\H {o} formulas.
Received by editor(s): July 31, 2008
Received by editor(s) in revised form: August 28, 2008
Published electronically: December 18, 2008
Additional Notes: Research supported by NSF grant DMS0400446 and U.S.-Israel BSF grant 2004353
Communicated by: Andreas Seeger
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.