[latexpage]
At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $latex x^* , a_{b_c}, \{a\}$:
$$ \begin{array}{ll}
A & B\\
\hline
C & D
\end{array}$$
$$
f_k = f(x_k),\: x_k = x^+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
$$
where $h$ is some step.
Then we interpolate points ${(x_k,fk)}$ by polynomial
\begin{equation} \label{eq:poly}
P{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\end{equation}
Its coefficients $latex {aj}$ 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: (eq:poly), (eq:sys).
Here is reference to non-existing equation (eq:unknown).