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[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 \label{eq:poly} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j} Its coefficients $\{a_j\}$ are found as a solution of system of linear equations: \label{eq:sys} \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2} Here are references to existing equations: (\ref{eq:poly}), (\ref{eq:sys}). Here is reference to non-existing equation (\ref{eq:unknown}).

Renders as:

At first, we sample in the ( is odd) equidistant points around :

where is some step.
Then we interpolate points by polynomial

(1)

Its coefficients are found as a solution of system of linear equations:

(2)

Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).