Encyclopedia > Erdös-Borwein constant

  Article Content

Erdös-Borwein constant

The Erdös-Borwein constant is the sum of the reciprocals of the Mersenne numbers.

By definition it is:

<math> E=\sum_{n=1}^{\infty}\frac{1}{2^n-1} \approx 1.60669 51524 15291 763... </math>

It can be proved that the following forms are equivalent to the former:

<math> E=\sum_{n=1}^{\infty}\frac{1}{2^{n^2}}\frac{2^n+1}{2^n-1} </math>

<math> E=\sum_{m=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{2^{mn}} </math>

<math> E=\sum_{n=1}^{\infty}\frac{\sigma_0(n)}{2^n} </math>

where <math>\sigma_0(n)</math> represents a multiplicative function, the number of positive divisors of the number <math>n</math>.

Paul Erdös showed that the constant E is an irrational number.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
French resistance

... tortured Moulin’s whereabouts out of him and Moulin was arrested (alongside others) in Caluire[?] in June 21. Moulin died after heavy torture in July 8 1943. After that, ...

 
 
 
This page was created in 167.9 ms