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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Normalizing orthogonal polynomials by using their recurrence coefficients
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by Alan G. Law and M. B. Sledd PDF
Proc. Amer. Math. Soc. 48 (1975), 505-507 Request permission

Abstract:

Polynomials ${P_n}(x)$ generated by a three-term recurrence relation with suitably restricted coefficients are orthogonal with respect to a (perhaps unknown) distribution $d\alpha (x)$ on the real line. An evaluation of $\int _a^b {P_n^2(x)d\alpha (x)}$ is given in terms of the coefficients in the recurrence relation. Knowledge of the distribution $d\alpha (x)$ is unnecessary.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 505-507
  • MSC: Primary 33A65
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0364707-2
  • MathSciNet review: 0364707