Recall the definition of the Gamma function:
![\[ \Gamma(s) = \int_{0^+}^{\infty} t^{s-1} e^{-t} \, dt \qquad \text{for} \quad s > 0. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-13c83b13d73d14725ac9d20affb552e7_l3.png "Rendered by QuickLaTeX.com")
Using integration by parts, prove the functional equation:
![\[ \Gamma(s+1) = s \Gamma(s). \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-f0addc2944749dc36a90a6753c4309a1_l3.png "Rendered by QuickLaTeX.com")
Then use mathematical induction to prove that for positive integers 
we have
![\[ \Gamma(n+1) = n!. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-6e44bba80dee8c4c149619058750804b_l3.png "Rendered by QuickLaTeX.com")
Incomplete.
Recall the definition of the Gamma function:
Using integration by parts, prove the functional equation:
Then use mathematical induction to prove that for positive integers we have
Incomplete.
It seems rori simply didn’t have time for this one, as otherwise it seems quite a straightforward application of integration by parts, and then use that result to prove the induction step.
let me see if I can give a good answer