Definition of the Gamma Function
\Gamma(s)=\int_{0}^{\infty}e^{-t}t^{s-1}dt
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\Gamma(s+1)=s\Gamma(s)
Most commonly known as an extension of the factorial Function to complex numbers, the Gamma Function is one of the most profound topics of study in Analytic Number Theory.
In this text, we give the definition, prove its main property and provide the analytic continuation to the whole complex plane.
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