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I know that there is a formula called Cauchy's integral formula for entire function $f$

$$f(a)=\frac{1}{2\pi i}\int_{C}\frac{f(s)}{s-a}ds$$

Where $C$ is a closure of a disc.

Is it possible that we consider different type of closed curve for example rectangle, and by special integral on this curve that we would calculate value of $f$ at any point inside this curve?

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Yes. Actually, if you read the statement of Cauchy's integral formula, you will find it works for any rectifiable curve. In particular, yes, rectangular paths are fine.

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    $\begingroup$ With arbitrary (rectifiable) curves you have to take the winding number into account. $\endgroup$ – Martin R Aug 29 '19 at 12:17
  • $\begingroup$ If we pick a rectangle, then how does the integral would like? Or it will remain with no changes? $\endgroup$ – mkultra Aug 29 '19 at 12:45
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    $\begingroup$ @mkultra No change. $\endgroup$ – saulspatz Aug 29 '19 at 12:48

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