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BibTeX entry
@Article{Auluck:2012:IPT,
author = "S. K. H. Auluck",
title = "On the Integral of the Product of Three {Bessel}
Functions over an Infinite Domain: {Fourier}-Space
Representation of Nonlinear Dynamics of Continuous
Media in Cylindrical Geometry",
journal = j-MATHEMATICA-J,
volume = "14",
number = "??",
pages = "??--??",
month = "????",
year = "2012",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
bibdate = "Sat Mar 15 08:18:46 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/mathematicaj.bib",
URL = "http://www.mathematica-journal.com/2012/12/on-the-integral-of-the-product-of-three-bessel-functions-over-an-infinite-domain/",
abstract = "Fourier-space representation of the partial
differential equations describing nonlinear dynamics of
continuous media in cylindrical geometry can be
achieved using Chandrasekhar--Kendall (C-K) functions
defined over infinite domain as an orthogonal basis for
solenoidal vector fields and their generating function
and its gradient as orthogonal bases for scalar and
irrotational vector fields, respectively. All
differential and integral operations involved in
translating the partial differential equations into
transform space are then carried out on the basis
functions, leaving a set of time evolution equations,
which describe the rate of change of the spectral
coefficient of an evolving mode in terms of an
aggregate effect of pairs of interacting modes computed
as an integral over a product of spectral coefficients
of two physical quantities along with a kernel, which
involves the following integral: involving the product
of three Bessel functions of the first kind of integer
order. This article looks at this integral's properties
using a semi-empirical approach supported by numerical
experiments. It is shown that this integral has
well-characterized singular behavior. Significant
reduction in computational complexity is possible using
the proposed empirical approximation to this
integral.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.mathematica-journal.com/",
}
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