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MRB constant : ウィキペディア英語版
MRB constant

The MRB constant, named after Marvin Ray Burns, is a mathematical constant for which no closed-form expression is known. It is not known whether the MRB constant is algebraic, transcendental, or even irrational.
The numerical value of MRB constant, truncated to 6 decimal places, is
: .
==Definition==

The MRB constant is related to the following divergent series:
: \sum_^ (-1)^k k^.
Its partial sums
: s_n = \sum_^n (-1)^k k^
are bounded so that their limit points form an interval () of length 1. The upper limit point 0.187859… is what is known as the MRB constant.〔 〕
The MRB constant can be explicitly defined by the following infinite sums:
: 0.187859\ldots = \sum_^ (-1)^k (k^ - 1) = \sum_^ \left((2k)^ - (2k-1)^\right).
There is no known closed-form expression of the MRB constant.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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