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EULER'S CONSTANT

The Euler's Constant, or Euler-Mascheroni's constant, is defined as the limit (as n goes to infinity) of

1 + 1/2 + 1/3 + 1/4 + 1/5 + ... + 1/n - log(n).
This constant is usually denoted by the lower-case Greek letter gamma g and is approximately

     0.577215664901532860

This constant appears occurs in a lot of places such as numbers theory, prime numbers, etc.  For example, the Euler's constant can be shown to be equal to the derivative of the gamma function evaluated at 1.

Another interesting appearance of this constant can be found in the equation:

Where e is 2.71828.. which the base for natural logarithm, p represents all prime numbers smaller than n.  This equation is called Merten's third theorem. 

More Mathematical Recreations

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