Is it possible to express a function in terms of a power series of any arbitrary function?

Question

A while ago a read on Twitter something about a theorem that allowed you to extend somehow the taylor saries to any arbitrary function, but I couldnt find it again and Im very interested in it. I was just wondering if anyone knows or if I just dont remember correctly what I saw. I remember it was something like this

$$ f(z)=\sum_{n=0}^{inf} a_n \frac{(z-\phi (z) )^n}{n!} $$

Answer 1

By the way I found it. It is called Bürmann's theorem. Here it is:Bürmanns Theorem