I'm just wondering, does anybody know of an analytic proof that shows that :

?

Or do we just accept that this is true?? (Sun)

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- May 18th 2008, 06:49 PMChris L T521Special Gamma Value
I'm just wondering, does anybody know of an analytic proof that shows that :

?

Or do we just accept that this is true?? (Sun) - May 18th 2008, 06:59 PMMathstud28
- May 18th 2008, 07:01 PMMathstud28
- May 18th 2008, 07:01 PMChris L T521
- May 18th 2008, 07:03 PMmr fantastic
- May 18th 2008, 07:03 PMTheEmptySet
- May 18th 2008, 08:04 PMKrizalid
See here.

Of course not.

Here's another proof:

Start by showing for that Let the integral is equal to find the area of a semicircle with radius hence

Now rearrange this to get what you want.

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Oops, I realized that you want to find and I computed Anyway, the link above I gave you contains another proof. - May 18th 2008, 08:56 PMNonCommAlg
here's my favorite proof of the so-called Gaussian integral:

let then:

in the first integral let to get: i.e. is constant.

hence thus call this result (1). on the other hand, from the

definition of it's easily seen that call this (2). now (1) and (2) complete the proof.