Math Wiki
Advertisement

A power series is a series in the form

Power series can be used to represent functions in the form

since this is the formula for an infinite geometric series. For example,

over the interval of convergence, which is

Functions can sometimes be differentiated or integrated to put them in a form where they can represented by a power series. For example,

so

An important application of power series is in Taylor and Maclaurin series.

Advertisement