On an integral related to biaxially anisotropic media
type: Item
instance of: scholarly article
title: On an integral related to biaxially anisotropic media
zbMATH Open document ID: 1015.33003
DOI: 10.1016/S0377-0427(02)00368-0
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 2003-02-23T00:00:00Z
review text: In the paper under review is analyzed the following integral related to biaxially anisotropic media of theoretical electromagnetics: \[ f(x,a, b,p,m,n)= \int^\infty_0 {y^p\over y^2+x^2} J_m(ay)J_n(by)dy, \tag{*} \] where \(a\) and \(b\) (real and positive numbers) are distances from the origin to the source and observations points, \(J_m\) and \(J_n\) stand for Bessel functions and \(m\), \(n\) and \(p\) are integers with \(p+m+n\) odd. The evaluation of the integral (*) when \(b\neq a\) is developed by means of contour-integral techniques and the results are then extended to the case \(b=a\). The continuity and differentiability of the integral (*) as well as its consideration as a function of the complex variable \(x\) are also treated. In the paper the authors also discuss several relations between \(f\) and the discontinuous integrals \(WS(a,b,\lambda, \mu,\nu)\) of Weber and Schafheitlin (Mellin transform of the product of two Bessel functions \(J_\mu (ay)J_\nu(by))\) [see \textit{G. N. Watson}, A treatise on the theory of Bessel functions, 2nd. ed., Cambridge Mathematical Library. Cambridge: Cambridge Univ. Press, chapter XIII (1995; Zbl 0849.33001)]. Some generalizations are finally studied.
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 26B05
zbMATH DE Number: 1872830
zbMATH Keywords: Bessel functions
zbMATH Keywords: infinite integrals
zbMATH Keywords: continuity
zbMATH Keywords: differentiability
reviewed by: Nácere Hayek
describes a project that uses: Mathematica
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00368-0
OpenAlex ID: W1964202872
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description: scientific article; zbMATH DE number 1872830