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Zeros of expansions in orthogonal polynomials

Published online by Cambridge University Press:  04 October 2011

A. Iserles  and
E. B. Saff
A. Iserles
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW
E. B. Saff
Affiliation:
Institute for Constructive Mathematics, University of South Florida, Tampa, U.S.A.
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Abstract

The theory of bi-orthogonal polynomials is exploited to investigate the location of zeros of truncated expansions in orthogonal polynomials. It turns out that, subject to additional conditions, these zeros can be confined to certain real intervals. Two general techniques are being used: the first depends on a theorem that links strict sign consistency of a generating function to loci of zeros and the second consists of re-expression of transformations from [3] in an orthogonal basis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 559 - 573
Copyright
Copyright © Cambridge Philosophical Society 1989

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