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Gauss' mean value theorem
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(Theorem)
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Let $\Omega$ be a domain in $\mathbb{C}$ and suppose $f$ is an analytic function on $\Omega$ Furthermore, let $C$ be a circle inside $\Omega$ with center $z_0$ and radius $r$ Then $f(z_0)$ is the mean value of $f$ along $C$ that is,
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"Gauss' mean value theorem" is owned by Johan.
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Cross-references: mean, radius, center, circle, analytic function, domain
There is 1 reference to this entry.
This is version 9 of Gauss' mean value theorem, born on 2003-04-28, modified 2004-03-20.
Object id is 4216, canonical name is GaussMeanValueTheorem.
Accessed 5229 times total.
Classification:
| AMS MSC: | 30E20 (Functions of a complex variable :: Miscellaneous topics of analysis in the complex domain :: Integration, integrals of Cauchy type, integral representations of analytic functions) |
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Pending Errata and Addenda
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