Lagrange notation: $f^{(0)}(x)$? Using Lagrange notation, is  $f^{(0)}(x)=f(x)$? Is this standard notation, or would one have to define $f^{(0)}(x)=f(x)$ first, before using it?
Aside: the context of the question is whether to include the first term within the summation when expressing the Taylor series and hence start at $n=0$, or to write it separately outside the summation and start the summation at $n=1$.
The former has been done here: https://en.wikipedia.org/wiki/Taylor_series#Definition

A definition of something is always good before using it, as happend in the wikipedia article: 

The derivative of order zero of $f$ is defined to be $f$ itself. 

So you can start summation at $n=0$ in Taylor series after refering to this definition. But you can put your mind at rest. Most mathematicians would expect that $f^{(0)}(x)=f(x)$ without definition.
