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Mathematics 19 Online
OpenStudy (anonymous):

Right ?

OpenStudy (dominantvampire):

wha-?

OpenStudy (anonymous):

??????

OpenStudy (dominantvampire):

let him type lol

OpenStudy (anonymous):

lol

OpenStudy (anonymous):

\[\Gamma \left(\frac{1}{2}\right)=\sqrt{\pi}\]\[\Gamma \left(\frac{n}{2}\right) \\~~ \\~~ \\ =\left(\frac{n-2}{2}\right)\left(\frac{n-4}{2}\right){\Huge....}\left(\frac{1}{2}\right)\Gamma \left(\frac{1}{2}\right) \\ =\left(\frac{n-2}{2}\right)\left(\frac{n-4}{2}\right){\Huge....}\left(\frac{1}{2}\right)\Gamma \left(\frac{1}{2}\right)\sqrt{\pi}\]

OpenStudy (anonymous):

the first line is the given statement

OpenStudy (anonymous):

oh boy, i'm outta here lol

OpenStudy (anonymous):

I made a typo in last line

OpenStudy (dominantvampire):

same, sorry, never studied this

OpenStudy (alexandervonhumboldt2):

@nincompoop @TuringTest @dan815

OpenStudy (anonymous):

last line should say \[\Gamma\left(\frac{n}{2}\right)=\left(\frac{n-2}{2}\right)\left(\frac{n-4}{2}\right){\Huge....}\left(\frac{1}{2}\right)\sqrt{\pi}\]

OpenStudy (anonymous):

where n is an odd integer

OpenStudy (fibonaccichick666):

gamma of n=(n-1)! so ...

OpenStudy (anonymous):

yes, I know that, but this isn't a factorial of an integer.

OpenStudy (fibonaccichick666):

sorry, my second didn't enter

OpenStudy (fibonaccichick666):

So my question is, how do you know that n-(2k)=1 for some k?

OpenStudy (anonymous):

yeah this is correct

OpenStudy (anonymous):

@fbi2015

OpenStudy (anonymous):

gamma(x+1)=xgamma(x) if x>0 comes directly from this formula

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