Construct of the form

∑_{n=0}^{∞} `a`_{n}x^{n}

where

`x` is a

*formal* variable and the

`a`_{n} are

coefficients (usually coming from a

field, but sometimes from more exotic objects. Using the standard

rules of

algebra we can perform formal operations on the series, like

addition and

multiplication; others may be possible, depending on where we get our coefficients from.

Sometimes we'll use a power series about `x`_{0}, by replacing "`x`" above with "(`x`-`x`_{0})" throughout.

In analysis we usually also demand that our power series converge in some neighbourhood.

All Taylor series (and MacLaurin series) are power series.