1. The problem statement, all variables and given/known data Find all functions f(z) satisfying a) f(z) is analytic in the disc |z-1| < 1, and b) f(n/(n+1)) = 1 - 1 / (2n^2 + 2n+1). 2. Relevant equations 3. The attempt at a solution One can deduce by algebraic re-arrangement that one solution is f(z) = 2z / (1+z^2). But how can I show that this function is the unique function satisfying this condition? Any hints?