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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Asymptotics for solutions of smooth recurrence equations


Authors: Attila Máté and Paul Nevai
Journal: Proc. Amer. Math. Soc. 93 (1985), 423-429
MSC: Primary 39A10; Secondary 41A60, 42C05, 58F08
MathSciNet review: 773995
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Abstract: It is shown that convergent solutions of a smooth recurrence equation whose gradient satisfies a certain "nonunimodularity" condition can be approximated by an asymptotic expansion. The lemma used to show this has some features in common with Poincaré's theorem on homogeneous linear recurrence equations. An application to the study of polynomials orthogonal with respect to the weight function $ \exp ( - {x^6}/6)$ is given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0773995-6
PII: S 0002-9939(1985)0773995-6
Keywords: Asymptotic expansion, orthogonal polynomials, recurrence equation
Article copyright: © Copyright 1985 American Mathematical Society