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Question Number 142301 by 777316 last updated on 29/May/21

Answered by Dwaipayan Shikari last updated on 29/May/21

$$\sin \left(\frac{\pi s}{2}\right)\mathrm{\Gamma }(1-s)=\sin \left(\frac{\pi s}{2}\right)\frac{\pi }{sin\left(\pi s\right)\mathrm{\Gamma }\left(s\right)}$$$$\underset{s\to 2n}{\lim }=\frac{\pi }{2\cos \left(\frac{\pi }{2}s\right)\mathrm{\Gamma }\left(s\right)}=\frac{\pi }{2\mathrm{\Gamma }\left(2n\right){(-1)}^n}$$

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