On the Regular Integral Solutions of a Generalized Bessel Differential Equation
The original Bessel differential equation that describes, among many others, cylindrical acoustic or vortical waves, is a particular case of zero degree of the generalized Bessel differential equation that describes coupled acoustic-vortical waves. The solutions of the generalized Bessel differentia...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/8919516 |
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| author | L. M. B. C. Campos F. Moleiro M. J. S. Silva J. Paquim |
| author_facet | L. M. B. C. Campos F. Moleiro M. J. S. Silva J. Paquim |
| author_sort | L. M. B. C. Campos |
| collection | DOAJ |
| description | The original Bessel differential equation that describes, among many others, cylindrical acoustic or vortical waves, is a particular case of zero degree of the generalized Bessel differential equation that describes coupled acoustic-vortical waves. The solutions of the generalized Bessel differential equation are obtained for all possible combinations of the two complex parameters, order and degree, and finite complex variable, as Frobenius-Fuchs series around the regular singularity at the origin; the series converge in the whole complex plane of the variable, except for the point-at-infinity, that is, the only other singularity of the differential equation. The regular integral solutions of the first and second kinds lead, respectively, to the generalized Bessel and Neumann functions; these reduce to the original Bessel and Neumann functions for zero degree and have alternative expressions for nonzero degree. |
| format | Article |
| id | doaj-art-2d7661d0da8a4d6e9d9adcdc13a06e5d |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2d7661d0da8a4d6e9d9adcdc13a06e5d2025-02-03T01:04:35ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/89195168919516On the Regular Integral Solutions of a Generalized Bessel Differential EquationL. M. B. C. Campos0F. Moleiro1M. J. S. Silva2J. Paquim3Center for Aeronautical and Space Science and Technology (CCTAE), IDMEC, LAETA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalCenter for Aeronautical and Space Science and Technology (CCTAE), IDMEC, LAETA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalInstituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalInstituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, PortugalThe original Bessel differential equation that describes, among many others, cylindrical acoustic or vortical waves, is a particular case of zero degree of the generalized Bessel differential equation that describes coupled acoustic-vortical waves. The solutions of the generalized Bessel differential equation are obtained for all possible combinations of the two complex parameters, order and degree, and finite complex variable, as Frobenius-Fuchs series around the regular singularity at the origin; the series converge in the whole complex plane of the variable, except for the point-at-infinity, that is, the only other singularity of the differential equation. The regular integral solutions of the first and second kinds lead, respectively, to the generalized Bessel and Neumann functions; these reduce to the original Bessel and Neumann functions for zero degree and have alternative expressions for nonzero degree.http://dx.doi.org/10.1155/2018/8919516 |
| spellingShingle | L. M. B. C. Campos F. Moleiro M. J. S. Silva J. Paquim On the Regular Integral Solutions of a Generalized Bessel Differential Equation Advances in Mathematical Physics |
| title | On the Regular Integral Solutions of a Generalized Bessel Differential Equation |
| title_full | On the Regular Integral Solutions of a Generalized Bessel Differential Equation |
| title_fullStr | On the Regular Integral Solutions of a Generalized Bessel Differential Equation |
| title_full_unstemmed | On the Regular Integral Solutions of a Generalized Bessel Differential Equation |
| title_short | On the Regular Integral Solutions of a Generalized Bessel Differential Equation |
| title_sort | on the regular integral solutions of a generalized bessel differential equation |
| url | http://dx.doi.org/10.1155/2018/8919516 |
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