Construct of the form
∑n=0∞ anxn
where
x is a
formal variable and the
an 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 x0, by replacing "x" above with "(x-x0)" throughout.
In analysis we usually also demand that our power series converge in some neighbourhood.
All Taylor series (and MacLaurin series) are power series.