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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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New integral identities for orthogonal polynomials on the real line
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by D. S. Lubinsky PDF
Proc. Amer. Math. Soc. 139 (2011), 1743-1750 Request permission


Let $\mu$ be a positive measure on the real line, with associated orthogonal polynomials $\left \{ p_{n}\right \}$ and leading coefficients $\left \{ \gamma _{n}\right \}$. Let $h\in L_{1}\left ( \mathbb {R}\right )$ . We prove that for $n\geq 1$ and all polynomials $P$ of degree $\leq 2n-2$, \begin{equation*} \int _{-\infty }^{\infty }\frac {P(t)}{p_{n}^{2}\left ( t\right ) } h\left ( \frac {p_{n-1}}{p_{n}} \left ( t\right ) \right ) dt=\frac {\gamma _{n-1}}{\gamma _{n}} \left ( \int _{-\infty }^{\infty }h\left ( t\right ) dt\right ) \left ( \int P\left ( t\right ) \text { }d\mu \left ( t\right ) \right ) . \end{equation*} As a consequence, we establish weak convergence of the measures on the left-hand side.
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Additional Information
  • D. S. Lubinsky
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
  • MR Author ID: 116460
  • ORCID: 0000-0002-0473-4242
  • Email:
  • Received by editor(s): March 23, 2010
  • Received by editor(s) in revised form: May 21, 2010
  • Published electronically: October 18, 2010
  • Additional Notes: This research was supported by NSF grant DMS1001182 and U.S.-Israel BSF grant 2008399
  • Communicated by: Walter Van Assche
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1743-1750
  • MSC (2010): Primary 42C05
  • DOI:
  • MathSciNet review: 2763762