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A contour is integrated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

... The integral over the contour C is thus 2 pi i times the residue which is pi. This means that: ... The contour integral is thus equal to -2 pi i exp(i pi alpha). ...

Using contour integral methods in the complex plane and the residue theorem. ... Using contour integral methods in the complex plane and the residue theorem. ∞. ...

... file) The poles are not inside the domain, therefore the integral over the contour is zero (the integrand is analytic everywhere inside the domain) (please see ...

... In this solution, we show how to compute the infinite sum Sum_{n=1}^infty{(-1)^{ n+1}/n^2} by computing an appropriate contour integral. 1. We wish to show that. ...

...integral in two parts and close the contours for the ... Cauchy's theorem that states that the integral of an analytic function along a closed contour is zero ...

... The contour integral is 2 pi i times the residue (the coefficient of t^(-1)) and is thus given by: ... The contour integral consists of the parts: ...

... A6. Evaluate the contour integral Rez dz γ. where γ is the unit circle z = eit (0 ≤ t ≤ 2π ). ... A7. Evaluate the contour integral ez dz z2 − 1 γ. ...

... think that this is similar to a Fresnel Integral (sin(x^2)). In that case, we would set z=e^(iz)^2, and then integrate over the special contour with regions I ...