Mathematics

N = ∫⋯∫

Docutils supports inline math with the prefix or postfix :math: role specificator, n! + sin(x²_n) and A_c = (π)/(4)d², as well as displayed math via the math directive:

f(ϵ) = (1)/(1 + exp⎛⎝(ε)/(k_BT)⎞⎠)

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

N = (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

M = ⎛⎜⎝ a b c d ⎞⎟⎠

is |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:

¹∫₀xⁿdx = (1)/(n + 1)

^m∑_n = 1n = (m(m + 1))/(2)

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

The Schrödinger equation

iħ(∂)/(∂t)Ψ = ĤΨ,

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

Math-Accents:

á `\acute{a}`	ṫ `\dot{t}`	γ̂ `\hat{\gamma}`
à `\grave{a}`	ẗ `\ddot{t}`	α̃ `\tilde{\alpha}`
x̆ `\breve{x}`	^⋯t `\dddot{t}`	^→ı `\vec{\imath}`
ǎ `\check{a}`	^‒a `\bar{a}`	^→R `\vec{R}`

Modulation Transfer Function:

MTF = ||(ℱ{s(x)})/(ℱ{s(x)}|_{ω_x = 0})|| = abs⎛⎝(∫^∞_− ∞s(x)e^iω_xxdx)/(∫^∞_− ∞s(x)dx)⎞⎠.

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_out(x) = s_in(x’)*s_δ(x − x’) = ∫s_in(x’)s_δ(x − x’)dx’

Cases with the AMSmath cases environment:

sgn(x) = ⎧⎨⎩ − 1 x < 0 − 1 x > 0