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单词 Laplace Limit
释义

Laplace Limit

The 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.html

Plouffe, 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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更新时间:2025/4/4 23:41:36