A power series (in one variable) is an infinite series of the form:

where *centered* at

can be written as a power series around the center

or, indeed, around any other center

## Exponential Function as a Power Series

The exponential function (in blue), and the sum of the first

In many situations

These power series arise primarily in real and complex analysis, but also occur in combinatorics (under the name of generating functions) and in electrical engineering (under the name of the

## Radius of Convergence

A power series will converge for some values of the variable

if this limit exists.