I was playing around in Desmos and found this interesting relationship. Where does it come from? I got $\frac1{x!(-x)!}= \frac{\sin{\pi x}}{\pi x}$. Why does this happen?
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1Have a look here: https://en.wikipedia.org/wiki/Gamma_function and here: https://en.wikipedia.org/wiki/Reflection_formula – Thomas Jan 12 '22 at 06:43
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2Does this answer your question? Why do we have this relation between $\frac{\sin \left(\pi x\right)}{\pi }$ and $x!$? – Gary Jan 12 '22 at 06:48
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2One shouldn't downvote such questions: they are natural ones ! – Jean Marie Jan 12 '22 at 08:16