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XXI—The Whittaker-Hill Equation and the Wave Equation in Paraboloidal Co-ordinates

Published online by Cambridge University Press:  14 February 2012

F. M. Arscott
F. M. Arscott
Affiliation:
University of Surrey.
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Synopsis

The problem considered is that of obtaining solutions of the Helmholz equation ∇2V + k2V = 0, suitable for use in connection with paraboloidal co-ordinates. In these co-ordinates the Helmholz equation is separable, and each of the separated equations is reducible to Hill's equation with three terms (the Whittaker-Hill equation). The properties of solutions of this equation are developed sufficiently to make possible the formal solution of simple boundary-value problems for paraboloidal surfaces, principally for the case k2 < 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 67 , Issue 4 , 1967 , pp. 265 - 276
Copyright
Copyright © Royal Society of Edinburgh 1967

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References

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