1. The problem statement, all variables and given/known data Find the power series for the function f(z) = (1-z)^-m Hint: Differentiation gives: f'(z) = m(1-z)^m-1 = m(1-z)^-1.f(z) or: zf'(z) + mf(z) = f'(z) Use the formula for differentiation of power series to determine the coefficients of the power series for f. 2. Relevant equations 3. The attempt at a solution Hi, here's my attempt so far: From real analysis, (1-x)^-1 = Σ(a_n).x^n, where the sum is from n=0 to infinity Differentiating:f'(x) (1-x)^-2 = Σ(a_n).n.(x^n-1) , from n=0 to infinity and so on until we get that the j-th derivative i.e. f^j.(x) = Σa_n(n C j).(x^n-j), where (n C j) is "n choose j" (binomial coefficient. Thus, substituting z for x and m for j, (1-x)^-m = Σa_n(n C m).(x^n-m), sum from 0 to infinity. --- I don't think this is correct; it seems too straightforward and I haven't used the hint. Can someone please point me in the right direction? Thanks for any help!