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?
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 ,
How do I go from here, anyone can give a hand is appreciated.
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!!
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.
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
(here I skipped the step where I evaluated and by using Euler's formula.
So , and we obtain the result by taking square root.