Due to (0x67270472) an analytic function \(f\) is locally given by
\begin{equation*} f(x)=\sum_{k=0}^{\infty} \frac{f^{(k)}(x_0)}{k!}(x-x_0)^k, \end{equation*}where \(x\) is in the convergence radius of \(f\) at \(x_0\). The series on the right hand side is called Taylor’s series.