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An example using Cauchy's theorem

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Let f be entire. Evaluate the integral from zero to 2 pi of f(z_0+re^(i theta)) e^(ik theta), where z_0 is a constant and k is a constant greater than or equal to 1.

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Solution Summary

Cauchy's theorem tells us that the integral of an entire function around a closed contour is zero. Attached is a 1/2 page solution written in Word with equations in Mathtype illustrating the use of this theorem. It also illustrates how substitution is often used to turn an integral into a contour integral to which the theorem may be applied.

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Solution is attached.

It sounds like you've done it right, and probably by exactly the method I'm about to show you!.

It is not explicitly stated, but I am assuming . (if , then and the question can be solved by integrating ...

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