Definition:Circle of Convergence

Definition

Let $\zeta \in \C$ be a complex number.

Let $\ds \map S z = \sum_{n \mathop = 0}^\infty a_n \paren {z - \zeta}^n$ be a complex power series in $z$ about $\zeta$.

Then the set of values of $z$ for which $\map S z$ converges is called the circle of convergence of $S$.

Also see

• Existence of Circle of Convergence of Power Series

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): circle of convergence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): power series
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): circle of convergence
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): power series