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High-frequency approximations to ellipsoidal wave functions

Published online by Cambridge University Press:  26 February 2010

F. M. Arscott  and
B. D. Sleeman
F. M. Arscott
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey.
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee, Dundee.
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Extract

When the Helmholz equation

is separated in ellipsoidal coordinates [1; §1.6] and the technique of separation of variables applied, there results the ordinary differential equation

known as the ellipsoidal wave equation or Lamé wave equation. In this equation k is the modulus of the Jacobian elliptic function sn z, and is related to the eccentricity of the fundamental ellipse of the ellipsoidal coordinates; a, b are separation constants, and the parameter q is connected with the wave number χ by

l being a real constant, the dimensional parameter of the coordinate system.

Type
Research Article
Information
Mathematika , Volume 17 , Issue 1 , June 1970 , pp. 39 - 46
Copyright
Copyright © University College London 1970

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References

1.Arscott, F. M., Periodic differential equations, (Pergamon Press, 1964).Google Scholar
2.Malurkar, S. L., Indian Jour. Phys., (9, 1935), 45.Google Scholar
3.Arscott, F. M., MRC Technical Summary report, 338 (University of Wisconsin, 1962).Google Scholar
4.Meixner, J.Schäfke, F. W., Mathieusche funktionen und Sphäroidfunktionen, (Springer, 1954).CrossRefGoogle Scholar
5.Sleeman, B. D., J. Inst. Math. Applics., 3 (1967), 4.CrossRefGoogle Scholar