Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Asymptotic expansion of $ \int\sp {\pi/2}\sb 0J\sp 2\sb \nu(\lambda\,{\rm cos}\,\theta)\,d\theta$

Author: R. Wong
Journal: Math. Comp. 50 (1988), 229-234
MSC: Primary 41A60; Secondary 33A40
MathSciNet review: 917830
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An asymptotic expansion is obtained, as $ \lambda \to + \infty $, for the integral

$\displaystyle I(\lambda ) = \int_0^{\pi /2} {J_v^2(\lambda \cos \theta )\;d\theta ,} $

where $ {J_v}(t)$ is the Bessel function of the first kind and $ v > - \tfrac{1}{2}$. This integral arises in studies of crystallography and diffraction theory. We show in particular that $ I(\lambda ) \sim \ln \lambda /\lambda \pi $.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 41A60, 33A40

Retrieve articles in all journals with MSC: 41A60, 33A40

Additional Information

Keywords: Asymptotic expansion, Bessel functions, Mellin transforms
Article copyright: © Copyright 1988 American Mathematical Society