Construct of the form
is a formal variable
and the an
s (usually coming from a field
, but sometimes from more exotic objects. Using the standard rule
s of algebra
we can perform formal operations on the series, like addition
; 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.