Let f(z) be analytic with a zero of order k .... 1. The problem statement, all variables and given/known data Let f(z) be analytic with a zero of order k at z0. Show that f '(z) has a zero of order k-1 at z0. 2. Relevant equations f(z) has a zero of order k at z0 if Ʃcn(z-z0)n (here n goes from k to ∞, and k ≠ 0) 3. The attempt at a solution Well, we of course f '(z) = kck(z-z0)k-1 + (k+1)ck+1(z-z0)k + .... , which looks to me like the definition of a function with a zero of order k at z0. ??????