Integral representation of the Euler-Mascheroni constant

Click on the image for a detailed proof

\gamma(s)=\int_{0}^{1}\frac{1-e^{-t}-e^{-\frac{1}{t}}}{t}\mathrm{d}t

There are several ways to express the Euler-Mascheroni constant as an integral. The one we explain today is used to prove various properties of the Gamma Function.

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On the number of primes less than a given quantity
On the number of primes less than a given quantity
The Bohr-Mollerup Theorem
The Bohr-Mollerup Theorem
Definition of the Gamma Function
Definition of the Gamma Function
Relation to the Sine Function
Relation to the Sine Function
Xi Reflection Formula
Xi Reflection Formula
Relation to the Gamma Function 1
Relation to the Gamma Function 1

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