GENERALIZATION OF THE THOMSON FORMULA FOR HOMOGENEOUS HARMONIC FUNCTIONS

It is shown that the Thomson formula for three-dimensional harmonic homogeneous functions can be generalized if, instead of purely algebraic linear expressions, one uses a linear algebraic form with the participation of the first order partial derivatives of the source function. The paper provides a...

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Bibliographic Details
Published in:St. Petersburg Polytechnical University Journal. Physics and Mathematics 2019-06, Vol.12 (2)
Main Authors: Berdnikov Alexander, Gall Lidia, Gall Nikolaj, Solovyev Konstantin
Format: Article
Language:eng ; rus
Subjects:
electrostatic field
harmonic function
homogeneous function
magnetostatic field
scalar potential
Online Access:Get full text
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Summary:It is shown that the Thomson formula for three-dimensional harmonic homogeneous functions can be generalized if, instead of purely algebraic linear expressions, one uses a linear algebraic form with the participation of the first order partial derivatives of the source function. The paper provides an exhaustive list of firtst order differentiating expressions that convert arbitrary three-dimensional harmonic functions, which is a homogeneous function in Euler terms, into new three-dimensional homogeneous harmonic functions.
ISSN:2405-7223
DOI:10.18721/JPM.12204