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Orthogonal Recurrence Polynomials and Hamburger Moments

Published online by Cambridge University Press:  20 November 2018

A. G. Law
A. G. Law*
Affiliation:
University of Saskatchewan, Regina, Saskatchewan
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A three-term recurrence

1

where An (n ≥ 0), Bn (n ≥ 0) and Cn (n ≥ 0) are real numbers for which AnCn+1 ≠0 (n ≥ 0), generates a sequence {Pn} of real polynomials in which Pn has degree exactly n.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 53 - 56
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Favard, J., Sur les polynomes de Tchebicheff, Comptes Rendus, Acad. Sci. Paris, 200 (1935), 2052-2053.Google Scholar
2. Law, A. G., Solutions of some countable systems of ordinary differential equations, Doctoral Dissertation, Georgia Inst. Tech., 1968.Google Scholar
3. Szegö, G., Orthogonal polynomials, 3rd ed., Colloq. Publ., Vol. XXIII, Amer. Math. Soc, Providence, R.I., 1967.Google Scholar