Definition:Euler-Mascheroni Constant

Definition
The Euler-Mascheroni constant $\gamma$ is the real number that is defined as:

where $\sequence {H_n}$ are the harmonic numbers and $\ln$ is the natural logarithm.

Also known as
This constant is otherwise known as Euler's constant but must not be confused with Euler's number.

It is also sometimes known as Mascheroni's constant.

Some sources denote it by the symbol $\mathrm C$.

Also see

 * Existence of Euler-Mascheroni Constant where its existence is demonstrated.


 * Euler's Integral Theorem, which proves that $H_n = \ln n + \gamma + \map \OO {\dfrac 1 n}$