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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 

(1)   \begin{equation*} 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:

(2)   \begin{equation*} \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: (1), (2).
Here is reference to non-existing equation (??).

…or something like this:

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