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, issue 1

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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https://doi.org/10.1155/2018/8919516

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:8919516

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