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Proceedings of the American Mathematical Society

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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
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.

References [Enhancements On Off] (What's this?)

  • [1] J. Favard, Sur les polynomes de Tchebicheff, C. R. Acad. Sci. Paris 200 (1935), 2052-2053.
  • [2] H. L. Krall and O. Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100-115. MR 10, 453. MR 0028473 (10:453a)
  • [3] A. G. Law, Solutions of some countable systems of ordinary differential equations, Doctoral Dissertation, Georgia Institute of Technology, 1968.

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Keywords: Orthogonal polynomials, three-term recurrence relation, normalization
Article copyright: © Copyright 1975 American Mathematical Society

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