Problem 1363 (difficulty: 9/10)

Let \(\displaystyle \Gamma(s)=\int_0^\infty x^{s-1} e^{-x}\dx\) and \(\displaystyle B(s,u)=\int_0^1 x^{s-1} (1-x)^{u-1} \dx\) be Euler's Gamma- and Beta functions. Show that

\(\displaystyle B(s,u) = \frac{\Gamma(s)\Gamma(u)}{\Gamma(s+u)}. \)

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