I am working on this problem below.

Prove that ,

So, I tried to compute , which I think is equal to

But here I need to show that , and I'm stuck on showing this. Can anyone give some help?

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- Nov 18th 2008, 11:58 PMnamelessguyGamma function
I am working on this problem below.

Prove that ,

So, I tried to compute , which I think is equal to

But here I need to show that , and I'm stuck on showing this. Can anyone give some help? - Nov 19th 2008, 04:33 AMDavid24
This should point you in the right direction,

Gamma function - Wikipedia, the free encyclopedia

please let me know if you require any further assistance

Great problem!

David - Nov 20th 2008, 02:37 AMnamelessguy
Thanks for your help David.

I already showed that

by a direct computation using the fact that . So, just take the absolute value of both sides then I got the result.

However,I'm still stuck with proving my original question. From the link you gave me, there are lots of ways to define the gamma function, so I think I should use the standard definition

Then I want to show ,

I have

How do I go from here, anyone can give a hand is appreciated. - Nov 20th 2008, 02:47 AMDavid24
Ahh you obviously didn't read the post in too much detail !! (j/j), there is a fantastic property of the gamma function in terms evaluating the conjugate of F(z) Whereby

Conjugate(F(z)) = F(Conjugate of z)

(I can prove if you want (more than happy to) but its a lot of work...)

Hope this points you in the right direction, if you need any further help please message me - this is a great problem!!

Regards,

David - Nov 20th 2008, 07:59 AMnamelessguy
- Nov 20th 2008, 09:08 AMDavid24
NamelessGuy,

I apologise if I caused any offence, It was not my intention to do so, I only commented on the 'Conjugate' property as I thought you may not have read it.

Please let me know how you got the solution out, I am highly interested in comparing methodologies.

Regards,

David - Nov 21st 2008, 01:22 AMDavid24
hey mate, have you got it out yet? cant wait to here the result!

- Nov 21st 2008, 02:18 AMnamelessguy
Nope, you didn't offense me at all. I'm here to learn and get help so any help is welcome and appreciate.

If you're asking about the solution I got for this. Yes, I did but I didn't prove the conjugation property of the gamma function.

This is how I did

We know that

Hence,

Now compute

(here I skipped the step where I evaluated and by using Euler's formula.

So , and we obtain the result by taking square root.