I want the integral exp(i*z)/(z*(z-1)*(z+1)*(z-i)^2*(z+i)^2) to be evaluated at |z| = 2. How do I get those bounds?
exp(i*z)/(z*(z-1)*(z+1)*(z-i)^2*(z+i)^2)
|z| = 2
From wikipedia see example:
f = (Exp[I*z]/(z*(z - 1)*(z + 1)*(z - I)^2*(z + I)^2) /. z -> 2*Exp[I t])*D[2 Exp[I t], t] // Simplify Integrate[f, {t, 0, 2*Pi}] // Expand (*-2 I \[Pi] + (I \[Pi])/E + (I E \[Pi])/2 + 1/2 I \[Pi] Cos[1]*)
Thank you for clarifying contour-integrals. However your implementation looks like code for Mathematica. Is there also a way to put it right into Wolfram|Alpha web?
I think as of today, Wolfram Alpha cannot do it yet.
