Definition:Functional Series

Definition

A functional series is a series of the form:

$\ds \sum \map {f_n} x$

such that the terms are functions of an independent variable $x$.

Region of Convergence

Let $S$ be a functional series of an independent variable $x$.

The region of convergence of $S$ is the set of values of $x$ for which $S$ is convergent.

Also see

• Results about functional series can be found here.

Sources

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