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Transfinite Diameter


\phi(z)=cz+c_0+c_1 z^{-1}+c_2 z^{-2}+\ldots

be an Analytic Function, Regular and Univalent for $\vert z\vert>1$, which maps $\vert z\vert>1$ Conformally onto the region $T$ preserving the Point at Infinity and its direction. Then the function $\phi(z)$ is uniquely determined and $c$ is called the transfinite diameter, sometimes also known as Robin's Constant or the Capacity of $\phi(z)$.

See also Analytic Function, Regular Function, Univalent Function

© 1996-9 Eric W. Weisstein