Docutils supports inline math with the prefix or postfix :math: role specificator, n! + \sin(x_n^2) and A_\text{c} = \frac{\pi}{4} d^2 , as well as displayed math via the math directive:

f(\epsilon) = \frac{1}{1 + \exp\left(\frac{\varepsilon}{k_\text{B}T}\right)}

Content may start on the first line of the directive, e.g.

N = \frac{\text{number of apples}}{7}

Equations can be labeled with a reference name using the :name: option. See eq:M and eq:schrödinger below.

The determinant of the matrix

\mathbf{M} = \left(\begin{matrix}a&b\\c&d\end{matrix}\right)

is |\mathbf{M}| = ad - bc .

More than one display math block can be put in one math directive. For example, the following sum and integral with limits:

\int_0^1 x^n dx = \frac{1}{n + 1}
\sum_{n=1}^m n = \frac{m(m+1)}{2}

LaTeX-supported Unicode math symbols can be used in math roles and directives:

The Schrödinger equation

i\hbar \frac{\partial }{\partial t}\Psi  = \hat{H}\Psi ,

with the wave function \Psi , describes how the quantum state of a physical system changes in time.

\acute{a} \acute{a} \dot{t} \dot{t} \hat{\gamma} \hat{\gamma}
\grave{a} \grave{a} \ddot{t} \ddot{t} \tilde{\alpha} \tilde{\alpha}
\breve{x} \breve{x} \dddot{t} \dddot{t} \vec{\imath} \vec{\imath}
\check{a} \check{a} \bar{a} \bar{a} \vec{R} \vec{R}

Modulation Transfer Function:

\text{MTF} = \left|\frac{\mathcal{F}\{s(x)\}}
                        {\mathcal{F}\{ s(x)\} |_{\omega _{x}=0}}\right|
           = \mathrm{abs}\left(\frac
                 {\int _{-\infty }^{\infty }s(x) \mathrm{e}^{\mathrm{i}\omega _{x}x}\mathrm{d}{x}}
                 {\int _{-\infty }^{\infty }s(x)\mathrm{d}{x}}

Math split over two lines: If a double backslash is detected outside a \begin{...} \end{...} pair, the math code is wrapped in an AMSmath align environment:

s_{\mathrm{out}}(x) & = s_{\mathrm{in}}(x') * s_\delta (x-x') \\
                    & = \int  s_{\mathrm{in}}(x')s_\delta (x-x')\mathrm{d}x'

Cases ("manually", with matrix environment):

\mathrm{sgn}(x) = \left\{\begin{matrix}
                    -1 & x<0\\
                    1 & x>0

Cases with the AMSmath cases environment (not (yet) supported by HTML writers with --math-output=MathML):

\mathrm{sgn}(x) = \begin{cases}
                    -1 & x<0\\
                     1 & x>0