EDB — 1KZ

[1KZ] Difficulty:*.Let \(g(z)=∑_{m=0}^∞ b_ m z^ m\) with non-zero radius of convergence \(r_ g\). Let \(I_ g⊂ ℂ\) be a zero-centered disk of radius less than \(r_ g\); so we defined a function \(g:I_ g→ℂ\). We assume \(g(0)=0\) and \(g'(0)≠ 0\). Assuming that the inverse \(f(y)=g^{-1}(y)\) can be expressed in Taylor series \(f(x)=∑_{n=0}^∞ a_ n x^ n\), compute the coefficients of the series of \(f\) starting from those of \(g\).