On a class of integrals involving a Bessel function times Gegenbauer polynomials
type: Item
instance of: scholarly article
title: On a class of integrals involving a Bessel function times Gegenbauer polynomials
zbMATH Open document ID: 1137.33303
DOI: 10.1155/2007/73750
author: Stamatis Koumandos
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/54107
review text: Summary: We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer. Some interesting special cases and applications of this result are obtained. In particular, we give a short proof of a recent result of \textit{A. A. R. Neves} et al. [J. Phys. A, Math. Gen. 39, No. 18, L293--L296 (2006; Zbl 1099.33004)] regarding the analytical evaluation of an integral of a Bessel function times associated Legendre functions. These integrals arise in problems of vector diffraction in electromagnetic theory.
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C47
Mathematics Subject Classification ID: 33C90
zbMATH DE Number: 5282439
MaRDI profile type: Publication
OpenAlex ID: W2034587218
cites work: Analytical results for a Bessel function times Legendre polynomials class integrals
cites work: Q5846799
cites work: Q4275389
cites work: Q4061445
description: scientific article; zbMATH DE number 5282439