I have a simple calculus question, (so simple it's actually embarrassing)
So I'm reading this article that says:
But I can't get that result!!!
Can anyone show me the intermediate steps please?
I assume that you are integrating with respect to . You mostly need the following identities
Then you find the limit as . It is 1/2 or -1/2 depending on whether or not. Suppose that . Then
The integral in the denominator is
Converting to trigonometric form, the top integral becomes
and the bottom integral becomes
The fraction of these simplifies to
The whole sum is now equal to
I'm not sure how one can proceed from here.
Thank you Vlasev,
I am getting quite similar results to yours, which is obviously different the one I expected!
My original reference is the appendix section of this paper:
The authors are quite well known in their field and the paper was published in a very high ranked conference, so I will be very surprised if their calculation is wrong.
Even thought they are well-known and the conference is highly-ranked, it's not guarantee that there won't be any mistakes. I'd say that there will be more mistakes in places where a derivation should be "obvious". The referees will probably not check. As for this, I don't know whether it's wrong or not.
Edit: I think their identity might well be wrong.