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.References
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J. Favard, Sur les polynomes de Tchebicheff, C. R. Acad. Sci. Paris 200 (1935), 2052-2053.
- H. L. Krall and Orrin Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100–115. MR 28473, DOI 10.1090/S0002-9947-1949-0028473-1 A. G. Law, Solutions of some countable systems of ordinary differential equations, Doctoral Dissertation, Georgia Institute of Technology, 1968.
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