Math & Physics Problems Wikia
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Problem

Let be a complex-valued function that is analytic inside and on a circle centered at . Use Cauchy's integral formula to prove Gauss' mean value theorem

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Gauss mean value theorem.gif

Solution

The equation for the circle is or . Thus, .

Consequently we can transform the Cauchy's integral formula in terms of .

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Remark: This formula is a mean value theorem because it has the form

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