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A complete asymptotic expansion of the jacobi functions with error bounds

A complete asymptotic expansion of the jacobi functions with error bounds In this paper we give a complete asymptotic expansion of the Jacobi functionsφ λ (α, β) (t) as λ→ + ∞. The method we employed to get the complete expansion follows that of Olver in treating similar problems. By using a Gronwall-Bellman type inequality for an improper integral in which the integrand is an unbounded function and contains a parameter, we get an error bound of the asymptotic approximation which is different from that of Olver's. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A complete asymptotic expansion of the jacobi functions with error bounds

Li, Xiuchun
Acta Mathematicae Applicatae Sinica , Volume 3 (4) – Jul 13, 2005
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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1987 by Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02008376
Publisher site
See Article on Publisher Site

Abstract

In this paper we give a complete asymptotic expansion of the Jacobi functionsφ λ (α, β) (t) as λ→ + ∞. The method we employed to get the complete expansion follows that of Olver in treating similar problems. By using a Gronwall-Bellman type inequality for an improper integral in which the integrand is an unbounded function and contains a parameter, we get an error bound of the asymptotic approximation which is different from that of Olver's.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 13, 2005

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