Maclaurin series of $f(g(x))$ I was doing some exercise about Maclaurin expansion when I notice something, I used to remember the series formula of some common functions with $x$ as argument, but when I had to calculate the expansion for the same function but with $x^2$ as argument, for example, I always recalculate the series from scratch.
Then I started to realise that I could have just substituted $x$ with $x^2$. So is it wrong to say that, given a polynomial function $P(x)$ which represent the series of Maclaurin for a function $f(x)$, the series of Maclaurin for $f(g(x))$ is equal to $P(g(x))$ when $g(x)$ approach to $0$? 
If it's not completely wrong can you give me some hints in order to understand when it's correct?

As always,
for this type of question
on generating functions,
the book "generatingfunctionology"
is a great reference.
It can be downloaded for free here:
https://www.math.upenn.edu/~wilf/DownldGF.html
