How do you find a power series representation for # f(z)=z^2 # and what is the radius of convergence?
A power series (centered at
so in this case,
In general, no manipulation is needed to find the power series of a polynomial function, as a power series is itself essentially a polynomial of infinite degree.
As for the radius of convergence, for any real value, the above power series has a single nonzero term which is equal to the square of that value, and thus does not diverge. This means the radius of convergence is infinite.