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# 5: Cauchy Integral Formula


Cauchy’s theorem is a big theorem which we will use almost daily from here on out. Right away it will reveal a number of interesting and useful properties of analytic functions. More will follow as the course progresses. We start with a statement of the theorem for functions. After some examples, we’ll give a generalization to all derivatives of a function. After some more examples we will prove the theorems. After that we will see some remarkable consequences that follow fairly directly from the Cauchy’s formula.

5: Cauchy Integral Formula is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jeremy Orloff via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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