Uniqueness of Analytic Continuation

1.6k Views Asked by At

I wasn't very well introduced to Analytic Continuations, but from what I have seen, showing that the analytic continuation is unique is pretty simple. In Real Analysis, from what I can imagine, there isn't a unique analytic continuation of a function, is that true? If so, why is it that we can so easily restrict the continuation of a complex function to be one and only one thing?