[latexpage]

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}

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}

\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}), (\ref{eq:sys}).

Here is reference to non-existing equation (\ref{eq:unknown}).