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kirbykirby
 3 years ago
Verifying the property of the Gamma function:
Gamma(n) = (n1)!
kirbykirby
 3 years ago
Verifying the property of the Gamma function: Gamma(n) = (n1)!

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kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.0\[\Gamma (\alpha)=\int\limits_{0}^{\infty}x^{\alpha1}e^{x}dx\] I understand how to get to the relationship \[\Gamma (\alpha)=(\alpha1)\Gamma (\alpha1)\] for any alpha >1 But I'm not sure how t get to :\[\Gamma (n)=(n1)!\] for n is a positive integer

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0really? you have done all the hard work!

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.0I dunno why I can't see this.. my brain is fried probably from doing the first part LOL

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that is \(n!\) can be defined as the recursion \(1!=1\) and \(n!=n(n1)!\)

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.0OH i see right!! Oh thank you. Haha oh my that was fairly simple :P

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah way way more simple than showing \(\Gamma(\alpha)=(\alpha1)\Gamma(\alpha 1)\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0like opening the jar after someone already loosened it

kirbykirby
 3 years ago
Best ResponseYou've already chosen the best response.0@satellite73 I couldn't help but wonder how do you keep your equations on the same line?
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