Reference for Lagrange inversion formula

Question

I am writing a piece of research where I use the Lagrange inversion formula for solving some equation. More precisely, for $y=f(x)$ where $f$ is analytic at $x=a$ and such that $f'(a)\neq 0$, we have \begin{equation} x = a + \sum_{n\ge 1}\frac{(y-f(a))^n}{n!}\lim_{x\rightarrow a}\partial_{x}^{n-1}\left(\frac{x-a}{f(x)-f(a)}\right)^n. \end{equation} which converges in a neighbourhood of $y=f(a)$.This is the form that can be found on Wikipedia https://en.wikipedia.org/wiki/Lagrange_inversion_theorem or many other non published sources, and seems the most convenient for me. However, I could not manage to find a reference stating this clearly (a book or so), with both this form involving a limit and consideration about the convergence of the series. Does any of you have one to use?