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

DOI:
https://doi.org/10.1090/S0025-5718-03-01553-9

Published electronically:
July 28, 2003

MathSciNet review:
2034117

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $W(x)=|x|^{\rho }$ 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

Email:
damelin@gsu.cs.gasou.edu

Keywords:
Asymptotics,
entire functions of finite and infinite order,
Erdős 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