Question

9. Suppose that f (z) has a simple pole at ao on a closed curve C, but is analytic elsewhere inside and on C except for poles at a finite number of interior points a1,a2,, (a) If the contour C is indented at ao by a circular arc with center at ao, show that the limiting form of the integral of f (x) around the indented contour is as the radius of the indentation tends to zero, regardless of whether the indentation excludes or includes the point ao (b) Obtain the evaluation (c) Obtain the evaluation ro sin(x + a)sin (a - a)dr İsin 2a r2-a2 0

Answer 1

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