Hi, I'm trying to solve a differential equation and I'm supposed to obtain a recursion formula for the coefficients of the power series solution of the following equation: w'' + (1/(1+z^2)) w = 0. The term 1/(1+z^2) I recognize as a geometric series and can be expressed as sum of 0 to infinity of: (-z^2)^n. But I'm having trouble multiplying it with w, which is also a power series. And also what is the radius of convergence for general initial conditions? Thanks.