Check out the sweeeet math we can do with mathjax!

An inline equation $2+3=1$, what?

And a display:

$$ \phi(3)=Jesus$$

Fractions:

$$x= \frac{1+y}{1+2z^2}$$

And some $\mathfrak{S}$

$$ A \cup B = 23$$

$$ =5 + 4$$

Something random…

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}

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}

{ P_{N-1}(x_k) = f_k },\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}

\end{equation}