Complex Analysis, Analytic Continuation

104 Views Asked by At

Is there any function $ f$ analytic for $|z|<1$, such that

$f(1/2)=1/3$ and $f(\frac{1}{2n+1})=\frac{1}{2n+1}$ for $n=1, 2, 3, ...$?

I'm thinking analytic continuation, but I can't seem to get anywhere...