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Laplace LimitThe value (Sloane's A033259) for which Laplace's formula for solving Kepler's Equation beginsdiverging. The constant is defined as the value at which the function
equals . The Continued Fraction of is given by [0, 1, 1, 1, 27, 1, 1, 1, 8, 2, 154, ...](Sloane's A033260). The positions of the first occurrences of in the Continued Fraction of are 2, 10, 35, 13,15, 32, 101, 9, ... (Sloane's A033261). The incrementally largest terms in the Continued Fraction are 1, 27, 154,1601, 2135, ... (Sloane's A033262), which occur at positions 2, 5, 11, 19, 1801, ... (Sloane's A033263).See also Eccentric Anomaly, Kepler's Equation References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/lpc/lpc.htmlPlouffe, S. ``Laplace Limit Constant.''http://www.lacim.uqam.ca/piDATA/laplace.txt. Sloane, N. J. A. Sequences A033259,A033260,A033261,A033262, andA033263in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.
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