# How do you find a power series representation for # f(z)=z^2 # and what is the radius of convergence?

##### 1 Answer

Nov 20, 2015

#### Explanation:

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.