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An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

William B. Jones ,
W. J. Thron  and
Nancy J. Wyshinski
William B. Jones
Affiliation:
Department of Mathematics University of Colorado Boulder, CO 80309-0426 U.S.A.
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Abstract

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It is known that the n-th denominators Qn (α, β, z) of a real J-fraction

where

form an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formula

the convergence being uniform on compact subsets of

Keywords

30B7033A6534E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 3 , 01 September 1992 , pp. 381 - 389
Copyright
Copyright © Canadian Mathematical Society 1992

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