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Transformations of Axes for Whittaker's Solution of Laplace's Equation

Published online by Cambridge University Press:  20 January 2009

G. B. Jeffery
G. B. Jeffery
Affiliation:
University College, London
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Whittaker has shown that a general solution of Laplace's equation, ∇2V = 0, may be expressed in the form

Since the harmonic property of a function is in no way dependent upon any particular set of axes it follows that the same solution must be capable of being expressed in the form

where X, Y, Z are any second set of rectangular coordinates.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , February 1916 , pp. 32 - 37
Copyright
Copyright © Edinburgh Mathematical Society 1917

References

* Whittaker, and Watson, , Modern Analysis, p. 3.Google Scholar