Displays

\section*{Displayed equations}
Displayed equations keep \TeX{}'s spacing, operator sizing, and limit placement:
\[
  \int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi},
  \qquad
  \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6},
  \qquad
  \zeta(s) = \prod_{p\ \mathrm{prime}} \frac{1}{1 - p^{-s}}.
\]
Nested subscripts, roots and large delimiters are sized as in print:
\[
  \lim_{n \to \infty} \left( 1 + \frac{x}{n} \right)^{\! n} = e^{x},
  \qquad
  \sqrt[3]{\,\frac{-q}{2} + \sqrt{\frac{q^2}{4} + \frac{p^3}{27}}\,}.
\]

\section*{Display families}
The width model is built from the finished boxes, whatever environment
produced them. This block shows the standard families.
\[
  \sum_{r=0}^{n} r = \frac{n(n+1)}{2}.
\]
\begin{equation}
  e^{i\pi}+1=0.
\end{equation}
\begin{gather}
  x+y=z, \\
  u+v=w.
\end{gather}
\begin{multline}
  a_1+a_2+a_3+a_4+a_5+a_6 \\
  {}+a_7+a_8+a_9+a_{10}=s.
\end{multline}
\begin{flalign}
  p&=q && r&=s, \\
  t&=u && v&=w.
\end{flalign}
\begin{alignat}{2}
  A&=B \qquad& C&=D, \\
  E&=F & G&=H.
\end{alignat}
\begin{equation}
  \begin{split}
    (x+y)^2 &= x^2+2xy+y^2, \\
    (x-y)^2 &= x^2-2xy+y^2.
  \end{split}
\end{equation}
\[
  \begin{aligned}
    \alpha&=\beta+\gamma, & \delta&=\epsilon, \\
    \zeta&=\eta,         & \theta&=\iota+\kappa,
  \end{aligned}
  \qquad
  \begin{gathered}
    m=n,\\
    r=s.
  \end{gathered}
\]