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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 (??).

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For the display environments, equation numbering is automatic, but this may be overridden and the number set explicitly with \tag{..} placed within the display expression.

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    \[ \boxed{f(x)=\int_1^{\infty}\frac{1}{x^2}\,\mathrm{d}x=1} \]

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compiles to

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