Let have a simple pole at and be an arc of a circle of radius , and angle then:
Also, something can be said about poles of other orders. See:
Art of Problem Solving Forum
has isolated singularity at
where is a closed path around
(This is directly from Residue Theorem)
My question is what is this integral if is rather an open semi-circular arc around
Do we have any formula/theorem for this?
May in some special case - (I'm more interested in finding the limit of this integral when the semi-circular arc in getting closer and closer to
Can I say ?
Is this result ever applicable?
Sorry, if my questions are vague but don't have a clear idea to ask a specific question at this moment