Hi. I am trying to evaluate the following integral:
where -1 < p < 1 and 0 < < 2*Pi. One can easily show the following:
When we transfer this over to the complex plane this means we have a branch point at x = 0 and a couple of simple poles at x = and x =
I am attempting to apply the pacman or keyhole contour here where the branch cut is made along the positive real axis.
I end up with the following:
A = = = I = I
But by the residue theorem we have:
I = =
but this cannot be right since we are integrating a real valued function over the real line... it shouldnt have any imaginary components. What have I done wrong?