Testing MathJax-LaTeX

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} \tag{1}
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} \tag{asdf}
\left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}

\begin{equation} \label{eq:sys2} \tag{asdf2}
\{ P_{N-1}(x_k) = f_k\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}
\end{equation}

\[\left(\frac{1}{2}\right) \qquad (\frac{1}{2})\]

Here are references to existing equations: \ref{eq:poly}, \eqref{eq:sys}.
Here is reference to non-existing equation \eqref{eq:unknown}.

 

\begin{equation}
X=
\begin{cases}
0, & \text{if}\ a=1 \\
1, & \text{otherwise}
\end{cases}
\end{equation}

 

$$ default, \it Italics, \bf bold,   \sf sans serif,   \tt typewriter, \rm default Roman, \it italics $$

$$horizontal spacing: back slash\ comma\, ! \! > \> : \: ; \; enspace \enspace quad \quad qquad \qquad end$$

$$hskip1point \hskip1pt hskip2point \hskip 2pt hskip10point \hskip10pt hskip3point \hskip 3pt 1ex \hspace{1ex} 1em \hspace{1em} 2em \hskip2em lengthofasdf \hphantom{<asdf>} backslash \ tilde ~ end$$

$$\tiny tiny$$

$$default$$

$$\scriptsize scriptsize \small small \normalsize normalsize or default, \large large$$

$$\normalsize normalsize or default, \large large$$

$$\Large Large \LARGE LARGE \huge huge \Huge Huge1$$

$$\Large  \LARGE  \huge  \Huge Huge2$$

$$\Huge Huge3$$

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