I thought of this question:
$f, g$ are functions that could be written as a power series in a disc with radius $R>0$, i.e. $$\forall |x|<r, f(x)=\sum a_n x^n, g(x)=\sum b_n x^n$$. If $b_0 = 0$, do we always have that $f(g(x))$ could be written as a power series in a disc containing 0?
I can't prove or find a counterexample, could anyone give me a hand?
Thanks a lot~