On the regular integral solutions of a generalized Bessel differential equation
type: Item
instance of: scholarly article
title: On the regular integral solutions of a generalized Bessel differential equation
zbMATH Open document ID: 1440.34092
DOI: 10.1155/2018/8919516
author: L. M. B. C. Campos
author: F. Moleiro
author: M. J. S. Silva
author: J. Paquim
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 34M03
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 6992035
Wikidata QID: Q115243929
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8919516
OpenAlex ID: W2898647413
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description: scientific article; zbMATH DE number 6992035