On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials
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...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/73750 |
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| _version_ | 1850168573957242880 |
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| author | Stamatis Koumandos |
| author_facet | Stamatis Koumandos |
| author_sort | Stamatis Koumandos |
| collection | DOAJ |
| description | 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 A. A. R. Neves et al. 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. |
| format | Article |
| id | doaj-art-a7cc67f58f5e4a789e7067a760a7a91f |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a7cc67f58f5e4a789e7067a760a7a91f2025-08-20T02:20:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/7375073750On a Class of Integrals Involving a Bessel Function Times Gegenbauer PolynomialsStamatis Koumandos0Department of Mathematics and Statistics, University of Cyprus, P. O. Box 20537, Nicosia 1678, CyprusWe 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 A. A. R. Neves et al. 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.http://dx.doi.org/10.1155/2007/73750 |
| spellingShingle | Stamatis Koumandos On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials International Journal of Mathematics and Mathematical Sciences |
| title | On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials |
| title_full | On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials |
| title_fullStr | On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials |
| title_full_unstemmed | On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials |
| title_short | On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials |
| title_sort | on a class of integrals involving a bessel function times gegenbauer polynomials |
| url | http://dx.doi.org/10.1155/2007/73750 |
| work_keys_str_mv | AT stamatiskoumandos onaclassofintegralsinvolvingabesselfunctiontimesgegenbauerpolynomials |