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Asymptotics of recurrence coefficients for orthonormal polynomials on the line--Magnus's method revisited

Author: S. B. Damelin
Journal: Math. Comp. 73 (2004), 191-209
MSC (2000): Primary 45M05, 33D45, 41A10, 65Q05, 42B05, 30D20, 35Q15, 15A42, 15A60
Published electronically: July 28, 2003
MathSciNet review: 2034117
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Abstract: We use Freud equations to obtain the main term in the asymptotic expansion of the recurrence coefficients associated with orthonormal polynomials $p_n(w^2)$ for weights $w=W\exp(-Q)$ on the real line where $Q$ is an even polynomial of fixed degree with nonnegative coefficients or where $Q(x) =\exp(x^{2m}),\, m\geq 1$. Here $W(x)=\vert x\vert^{\rho}$ for some real $\rho>-1$.

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Additional Information

S. B. Damelin
Affiliation: Department of Mathematics and Computer Science, Georgia Southern University, P. O. Box 8093, Statesboro, Georgia 30460

Keywords: Asymptotics, entire functions of finite and infinite order, Erd\H{o}s weights, Freud weights, orthogonal polynomials, recurrence coefficients
Received by editor(s): September 7, 2001
Received by editor(s) in revised form: June 19, 2002
Published electronically: July 28, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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