Question

Verifying the property of the Gamma function:
Gamma(n) = (n-1)!

Answer 1

\[\Gamma (\alpha)=\int\limits_{0}^{\infty}x^{\alpha-1}e^{-x}dx\]
I understand how to get to the relationship \[\Gamma (\alpha)=(\alpha-1)\Gamma (\alpha-1)\] for any alpha >1
But I'm not sure how t get to :\[\Gamma (n)=(n-1)!\] for n is a positive integer

Answer 2

really? you have done all the hard work!

Answer 3

I dunno why I can't see this.. my brain is fried probably from doing the first part LOL

Answer 4

yeah i guess so

Answer 5

\(n!=n(n-1)!\)

Answer 6

that is \(n!\) can be defined as the recursion \(1!=1\) and \(n!=n(n-1)!\)

Answer 7

OH i see right!! Oh thank you. Haha oh my that was fairly simple :P

Answer 8

Thanks :)!!

Answer 9

yeah way way more simple than showing \(\Gamma(\alpha)=(\alpha-1)\Gamma(\alpha -1)\)

Answer 10

For sure!!!

Answer 11

yw

Answer 12

like opening the jar after someone already loosened it

Answer 13

@satellite73 I couldn't help but wonder how do you keep your equations on the same line?