What is it about?
We consider the integral \epsilon_b (k,K) = \int_0^\infty x*exp( \eta*x^2)*J_b(K*x)*Y_b(k*x)dx where, K, k and b are all positive real numbers. We reduce this integral to a linear combination of two integrals. The first of these is an exponential integral, which can be expressed as a difference of two Shkarofsky functions, or can easily be evaluated numerically. The second is the original integral, but with k and K both replaced by kK. We express this as a Meijer G function, and then reduce it to the sum of an associated Bessel function and a modified Bessel function.
Featured Image
Photo by Ries Bosch on Unsplash
Why is it important?
This integral was encountered in a Physical problem of scattering of electromagnetic waves by a square array of perfectly conducting cylinders. Given the citation rate, it appears in other applications.
Perspectives
This integral found long ago became part of the Maple Computer algebra system and confirms that solutions to integrals are possible by converting the integrands to the Meijer G function.
Dr Tony Cyril Scott
RWTH-Aachen University
Read the Original
This page is a summary of: On a bessel function integral, Applicable Algebra in Engineering Communication and Computing, September 1992, Springer Science + Business Media,
DOI: 10.1007/bf01294334.
You can read the full text:
Resources
Contributors
The following have contributed to this page
