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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.
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