Trying to use residual theorem for integrating ellipse perimeter.
Can I use the residual theorem for the ellipse perimeter? The calculation process I've followed so far
If it cannot use the residual theorem, how to prove this inside function is not analytic in region $|z|\le 1$?
If I can use the residual theorem, what is the order of pole for $z=0$?
Is it possible to use the Laurent expansion to find the residual at $z=0$? I used the Laurent expansion but cannot get the correct answer.
