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Proceedings of the American Mathematical Society

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

 

 

Normalizing orthogonal polynomials by using their recurrence coefficients


Authors: Alan G. Law and M. B. Sledd
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0364707-2
Keywords: Orthogonal polynomials, three-term recurrence relation, normalization
Article copyright: © Copyright 1975 American Mathematical Society