[latexpage]

you may always place a LaTeX expression within shortcodes everywhere on the site. Attribute tags are allowed: [latex attrs]...[/latex].

x^2 + y^2 &= 1 y &= \sqrt{1 - x^2} (Could not format equation due to MathJax error)

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}

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}

\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: (\ref{eq:poly}), (\ref{eq:sys}).

Here is reference to non-existing equation (\ref{eq:unknown}).

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.

A number of options may be set for an expression with attribute tags such as size, color, background, align, as arguments of \quicklatex{} placed within the expression:

\quicklatex{color="#00ff00" size=25}

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

\]

Compilation of an expression may be suppressed, showing instead the LaTeX source, by preceding the expression with a !.

For mathematical graphs you may use tikzpicture and pgfplots, e.g. :

[+preamble]

\usepackage{pgfplots}

\pgfplotsset{compat=newest}

[/preamble]

\begin{axis}

\addplot3[surf,domain=0:360,samples=40] {cos(x)*cos(y)};

\end{axis}

\end{tikzpicture}