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`x`^{a} has a power series expansion
about `x`_{0}=1. (We shouldn't expect that this function have a power series
expansion centered on `x`_{0}=0, since for general real `a`, `x`^{a}
isn't even defined for `x=0`.)`x`^{a} is equal to this
series.
All it establishes is that this is the *only* power series which `x`^{a}
could possibly be equal to. But but now we have something something concrete to work with,
and we can use other tricks to
prove the two functions are equal
.

Example:

We shall show that the power function
First, let's consider what the power series for `x ^{a}` could possibly be. If it
is in fact true that

Of course computing the Taylor Series in no way proves that