Question

Special Function

Answer 1

How to prove this

Answer 2

Should I use
\[\Gamma (p) \Gamma(1-p) = \frac{ \pi }{ \sin \pi p } \]
???

Answer 3

@sirm3d

Answer 4

@.Sam.

Answer 5

have idea @.Sam. ??

Answer 6

\[\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}=\beta(x,y)=\int_0^1t^{x-1}(1-t)^{y-1}\mathrm dt \]
set \[x=p,y=1-p\] and solve the definite integral