Hello /sci/ I need help with the problem in the picture. I need to show that this equality is true with the given value Gamma(1/2)=sqrt(pi).
Now where do I even begin with this? I've only found a post at
http://math.stackexchange.com/questions/1154366/gamma-function-proof-of-gamma-%CE%931-2-sqrt-pi
but it doesn't really help me. Any hints here please? Thanks.
>>8083291
With your given value, n is 0. Just plug in and remember 0! is defined as 1.
Does the recursion formula not work for non-integers?
Induction.
>>8083291
At a glance I'd: take the definition of the gamma function, integrate by parts n-times, the final integral should just be the standard Gaussian integral.
It depends on what you've got to work with OP. Any identities, etc.? Like the ones in wikipedia or that article you point to?
Okay guys thanks for the replies.
I won't lie, this is pretty tough. I have found a suitable source:
http://www.jekyll.math.byuh.edu/courses/m321/handouts/gammaproperties.pdf
At page 3 this problem is worked, though the last step differs from mine. If all fails, I will just copy it. Perhaps you could help me trying to combine this last step?
I have also thought about gaussian integrals and one identity I often see is Γ(n+1)=nΓ(n). Besides that, we haven't got anything to work with.
>>8083319
Yes, that's why we like to use gamma to extend factorials
>>8083339
The last line of that example is equivalent to the formula you posted in the OP
>>8083342
Oh I see, thanks. Is the gamma function of any importance later on? If yes, then I need to put more effort into this.
>>8083349
It's just an interesting function. It can be used as a nice example for things like analytic continuation in complex analysis, but it's not vital for anything.
>>8083358
I understand. Well, I'm off then. Thank you all for the effort!
