At first, we sample $$f(x)$$ in the \(N\) ($N$ is odd) equidistant points around \(x^*\):

\[

f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}

\]

where \(h\) is some step.

Then we interpolate points \((x_k,f_k)\) by polynomial

\begin{equation}

\label{eq:poly} \tag{1}

P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}

\end{equation}

Its coefficients \(a_j\) are found as a solution of system of linear equations:

\begin{equation} \label{eq:sys} \tag{2}

\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}

\end{equation}

Here are references to existing equations: \ref{eq:poly}, \eqref{eq:sys}.

Here is reference to non-existing equation \eqref{eq:unknown}.