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Proof of Estimates

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|int(Log(z)/(z^2) dz, Cr| is less than or equal to 2pi((pi + ln(R))/R)

where Cr = {z|z = Re^i(theta), theta is an element of [0, 2pi]} and R > 1

In words: show that the following estimates hold The absolute value of the integral of Log(z) over z squared integrated w.r.t z from Cr is less than or equal to 2 pie times pie plus natural log of R over R.

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Solution Summary

In this solution, we show that the given estimates hold.

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