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Mathematics of Computation

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On the asymptotic evaluation of $ \int\sp {\pi/2}\sb 0J\sp 2\sb 0(\lambda\,{\rm sin}\,x)dx$

Authors: Basil J. Stoyanov and Richard A. Farrell
Journal: Math. Comp. 49 (1987), 275-279
MSC: Primary 41A60; Secondary 65D30
MathSciNet review: 890269
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Abstract: The asymptotic behavior of the integral

$\displaystyle I(\lambda ) = \int_0^{\pi /2} {J_0^2(\lambda \sin x)\,dx} $

is investigated, where $ {J_0}(x)$ is the zeroth-order Bessel function of the first kind and $ \lambda $ is a large positive parameter. A practical analytical expression of the integral at large $ \lambda $ is obtained and the leading term is $ (\ln \lambda )/(\lambda \pi )$.

References [Enhancements On Off] (What's this?)

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Keywords: Asymptotic expansion, Bessel functions
Article copyright: © Copyright 1987 American Mathematical Society

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