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To prove :

$(n-1)\cdot\Gamma ( n-1)=(n-1)!$ ; for every $n>1$

Also , is $\Gamma (n) = (n-1)!$ a derived conclusion or part of the definition of gamma functions ?

R_D
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Nikhil Kapoor
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    https://proofwiki.org/wiki/Gamma_Difference_Equation – Zubzub Sep 26 '16 at 15:11
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    There are multiple definitions of the $\Gamma$ function, for instance through the Bohr-Mollerup theorem, through the integral $\int_{0}^{+\infty}x^s e^{-x},dx $ or through Euler's product. Which one is the the definition you are using? – Jack D'Aurizio Sep 26 '16 at 15:21

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