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 for weights on the real line where is an even polynomial of fixed degree with nonnegative coefficients or where . Here for some real .

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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

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

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