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Homework Statement
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).
Homework Equations
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?