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On two-centred expansions in cylindrical polar co-ordinates

Published online by Cambridge University Press:  26 February 2010

R. Shail
R. Shail
Affiliation:
Department of Applied Mathematics. University of Liverpool.
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Extract

In a recent paper (Shail [1]) the present author considered the problem of finding a two-centred expansion of the retarded Helmholtz Green's function This work formed an extension to that of Carlson and Rushbrooke [2] (also Buehler and Hirschfelder [3]) on the Coulomb Green's function and arose out of considerations of the interaction energy of two charge distributions taking account of electromagnetic retardation. The two-centred expansion obtained in [1] took the form of a double Taylor series, each term being interpreted as a Maxwell multipole—multipole interaction energy between two “charge” distributions coupled through a retarded scalar field. The first few terms in the expansion were also given in spherical polar coordinates.

Type
Research Article
Information
Mathematika , Volume 8 , Issue 1 , June 1961 , pp. 69 - 78
Copyright
Copyright © University College London 1961

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References

1.Shail, R., Mathematika, 6 (1959), 108.Google Scholar
2.Rushbrooke, C. and Carlson, B. C., Proc. Cambridge Phil. Soc., 46 (1950), 626.Google Scholar
3.Beuhler, R. J. and Hirschfelder, J. O., Phys. Rev., 83 (1951), 628.CrossRefGoogle Scholar
4.Watson, G. N., Theory of Bessel functions (Cambridge, 1944).Google Scholar
5.Sommerfeld, A., Partial differential equations (Academic Press Inc., 1949).Google Scholar
6.Smythe, W. R., Static and dynamic electricity (McGraw-Hill, 1950).Google Scholar