It is often useful to shift the origin of a power series, i.e., consider
a power series expanded about a different point.
is called a power series centered at
, or ``a power series about
Here conceptually we are treating
like we treated 0
Power series can be written in different ways, which have different
advantages and disadvantages. For example,
Notice that the second series converges for
, whereas the first converges
, which isn't nearly as good.