Relation to the Sine Function
\Gamma(s)\Gamma(1-s)=\frac{\pi}{\sin(\pi s)}
\Downarrow
\Gamma(s)\Gamma(-s)=-\frac{\pi}{s\sin(\pi s)}
\Gamma(1+s)\Gamma(1-s)=\frac{\pi s}{\sin(\pi s)}
These Relations between the Gamma Function and the Sine Function are some of the most commonly used.
The demonstration we propose relies heavily on Euler’s Infinite Product.
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