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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$$E = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{2^k-1} = 1.606695152415291763\ldots$$
 
$$E = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{2^k-1} = 1.606695152415291763\ldots$$
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Note that the numbers in the denominator in this sum are the [[Mersenne numbers]].
  
 
=Properties=
 
=Properties=
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[[Erdős-Borwein Constant is irrational]]<br />
<strong>Theorem:</strong> $E$ is irrational
 
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<strong>Proof:</strong> █
 
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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

References

Paul Erdős - On Arithmetical Properties of Lambert Series