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21.—Asymptotic Evaluation of Certain Integral Formulae for Ellipsoidal Wave Functions*

Published online by Cambridge University Press:  14 February 2012

B. A. Hargrave  and
B. D. Sleeman
B. A. Hargrave
Affiliation:
Department of Mathematics, University of Aberdeen
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee.
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Synopsis

Although integral equations and relations for ellipsoidal wave functions have been known for some time, it had previously been impossible to obtain asymptotic estimates for these integrals, with large wave parameter, as the available asymptotic expansions for the integrand were non-uniform. However, uniform asymptotic expansions have recently been calculated for the functions occurring in the integrand, and these expansions are now used to determine asymptotic expansions for ellipsoidal wave functions of the third kind. A different type of normalisation is proposed for ellipsoidal wave functions and this is compared with previous normalisations by evaluating asymptotically a double integral.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 3 , 1975 , pp. 257 - 269
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

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