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On Kepler's equation

Published online by Cambridge University Press:  24 October 2008

T. M. Cherry
T. M. Cherry
Affiliation:
University of Melbourne, Australia
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Extract

1. Kepler's equation

has, when θ, x are real with 0 < x < 1, just one real root ξ = ξ*(θ, x). For this root there are the well-known formulae, dating from Lagrange and Bessel,

The objects of this paper are (i) to obtain analogous formulae for the unreal roots ξ of the equation, and (ii) to sum the conjugates (as Fourier series in θ) of the series on the right of (2) and (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 1 , January 1955 , pp. 81 - 91
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

† It may be emphasized that (38) is not an analytic continuation of (31); it is got by combining a continuation of (8) with a continuation, along a different path, of the conjugate of (8).