Difference between revisions of "Erdős-Borwein Constant"
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(Created page with "$$E = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{2^k-1} = 1.606695152415291763\ldots$$ =Properties= <div class="toccolours mw-collapsible mw-collapsed"> <strong>Theorem:</str...") |
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$$E = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{2^k-1} = 1.606695152415291763\ldots$$ | $$E = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{2^k-1} = 1.606695152415291763\ldots$$ | ||
| + | Note that the numbers in the denominator in this sum are the [[Mersenne numbers]]. | ||
=Properties= | =Properties= | ||
| − | + | [[Erdős-Borwein Constant is irrational]]<br /> | |
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=References= | =References= | ||
[http://www.renyi.hu/~p_erdos/1948-04.pdf Paul Erdős - On Arithmetical Properties of Lambert Series] | [http://www.renyi.hu/~p_erdos/1948-04.pdf Paul Erdős - On Arithmetical Properties of Lambert Series] | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 17:44, 24 June 2016
$$E = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{2^k-1} = 1.606695152415291763\ldots$$ Note that the numbers in the denominator in this sum are the Mersenne numbers.
Properties
Erdős-Borwein Constant is irrational
