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Cauchy-Hadamard Theorem

The Radius of Convergence of the Taylor Series

\begin{displaymath}
a_0+a_1z+a_2z^2+\ldots
\end{displaymath}

is

\begin{displaymath}
r={1\over\overline{\lim\limits_{n\to\infty}} (\vert a_n\vert)^{1/n}}.
\end{displaymath}

See also Radius of Convergence, Taylor Series




© 1996-9 Eric W. Weisstein
1999-05-26