On the Regular Integral Solutions of a Generalized Bessel Differential Equation

L. M. B. C. Campos, F. Moleiro, M. J. S. Silva and J. Paquim

Advances in Mathematical Physics, 2018, vol. 2018, 1-9

Abstract:

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:8919516

DOI: 10.1155/2018/8919516

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