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A simple method of summing Bessel series

Published online by Cambridge University Press:  24 October 2008

J. A. Greenwood
J. A. Greenwood
Affiliation:
Department of Mechanical Engineering, University of Liverpool
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Abstract

A simple formula is derived for transforming the slowly convergent series involving Bessel functions which arise in axially symmetric potential problems into more rapidly convergent series. Using it, sums of series previously found by elaborate special methods may be obtained by direct substitution. The necessary numerical coefficients are given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 705 - 710
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Bouwkamp, C. J. & de Bruijn, N. G.J. Appl. Phys. 18 (1947), 562–577.CrossRefGoogle Scholar
(2)Knight, R. C.Quart. J. Math. Oxford 7 (1936), 124–133.CrossRefGoogle Scholar
(3)Smythe, W. R.J. Appl. Phys. 24 (1953), 70–73.CrossRefGoogle Scholar
(4)Watson, G. N.Proc. Roy. Soc. A 130 (1931), 29–37.Google Scholar
(5)Watson, G. N.Theory of Bessel functions (Cambridge, 1944).Google Scholar