1. The problem statement, all variables and given/known data Find the power-series expansion about the given point for the function; find the largest disc in which the series is valid. f(z) = z^3 + 6z^2-4z-3 about z0=1. 2. Relevant equations 3. The attempt at a solution The series is fine. Since it's a polynomial, there are only three non-zero terms. I get: f(x) = 11(x-1) + 9(x-1)^2 + (x-1)^3. But I am very confused about the second part of the problem, the disc. I know that as a consequence of Cauchy's theorem, if f is analytic in a domain and there is a disk of some radius, say r, inside the domain, then f can be written as a (convergent) power series inside the disc. But I don't see how to find the disk! Unless it can be simply written as |x-x0| <= r. This kind of makes sense because you'd want the disc to be able to shrink about the point x0, where the expansion is going around. OR: Should be coefficients in the power series be something other than the normal I get from Taylor series? Is there some special technique that I'm not using?