Taylor expansion allows us to convert non-polynomial form of any function into polynomial form (though the function itself may not be polynomial, as the polynomail can contain infinite terms.).
The question, is this Taylor expansion the only way to do this?
Edit: I am changing the question into the following:
Suppose that there is a function $f(x)$. Is there a way to create a power series that equals to $f(x)$ without using Taylor expansion?