Here's the question: Consider the function f defined uniquely by the relation
Show that f has a series expansion in powers of x with strictly positive radius. (Hint: consider where and )
So far I figured out that , but that's about it. I tried "Taylor-expanding" these different functions, but can't do it about 0 and so it gets complicated. Also i am not too sure about composing the functions. It seems you can do it with formal power series, but i don't know for this particular problem.
I could possibly argue the existence of the series using some theorems, but the next question ask to compute the series for f as far as the term in , so I guess I really have to find a series expansion explicitely.
I would be thankful if anyone could tell me how I should start working on this...