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Integral equations and relations for Lamé functions and ellipsoidal wave functions

Published online by Cambridge University Press:  24 October 2008

B. D. Sleeman
B. D. Sleeman
Affiliation:
Department of Mathematics, The University, Dundee
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Abstract

Non-linear integral equations and relations, whose nuclei in all cases is the ‘potential’ Green's function, satisfied by Lamé polynomials and Lamé functions of the second kind are discussed. For these functions certain techniques of analysis are described and these find their natural generalization in ellipsoidal wave-function theory. Here similar integral equations are constructed for ellipsoidal wave functions of the first and third kinds, the nucleus in each case now being the ‘free space’ Green's function. The presence of ellipsoidal wave functions of the second kind is noted for the first time. Certain possible generalizations of the techniques and ideas involved in this paper are also discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 113 - 126
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

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