Latex - Formulas

Ref: http://www.personal.ceu.hu/tex/cookbook.html

Inline and Displayed Formulas

$x=\frac{1+y}{1+2z^2}$ (inline)
$$x=\frac{1+y}{1+2z^2}$$ (displayed)
$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$ (inline)
$$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$$ (displayed)
$\displaystyle \int_0^\infty e^{-x^2} dx$ (inline)
$$ \frac{1}{\displaystyle 1+ \frac{1}{\displaystyle 2+ \frac{1}{\displaystyle 3+x}}} + \frac{1}{1+\frac{1}{2+\frac{1}{3+x}}} $$

Spaces and Text in Formulas

$\sqrt{2} \sin x$, $\sqrt{2}\,\sin x$
$\int \!\! \int f(x,y)\,\mathrm{d}x\mathrm{d}y$
$$ \mathop{\int \!\!\! \int}_{\mathbf{x} \in \mathbf{R}^2} \! \langle \mathbf{x},\mathbf{y}\rangle \,d\mathbf{x} $$
$$ x_1 = a+b \mbox{ and } x_2=a-b $$
$$ x_1 = a+b ~~\mbox{and}~~ x_2=a-b $$

Multiple Line Equations

\begin{eqnarray} y &=& x^4 + 4 \nonumber \\ &=& (x^2+2)^2 -4x^2 \nonumber \\ &\le&(x^2+2)^2 \end{eqnarray}
\begin{eqnarray*} e^x &\approx& 1+x+x^2/2! + \\ && {}+x^3/3! + x^4/4! + \\ && + x^5/5! \end{eqnarray*}
\begin{eqnarray*} \lefteqn{w+x+y+z = }\\ && a+b+c+d+e+\\ && {}+f+g+h+i \end{eqnarray*}
\begin{eqnarray*} x&=&\sin \alpha = \cos \beta\\ &=&\cos(\pi-\alpha) = \sin(\pi-\beta) \end{eqnarray*}
{\setlength\arraycolsep{0.1em} \begin{eqnarray*} x&=&\sin \alpha = \cos \beta\\ &=&\cos(\pi-\alpha) = \sin(\pi-\beta) \end{eqnarray*} }
$$\setlength\arraycolsep{0.1em} \begin{array}{rclcl} x&=&\sin \alpha &=& \cos \beta\\ &=&\cos(\pi-\alpha) &=& \sin(\pi-\beta) \end{array} $$

Formula Numbering

\begin{equation} x=y+3 \label{eq:xdef} \end{equation} In equation (\ref{eq:xdef}) we saw $\dots$
\usepackage{leqno} ... \begin{equation} x=y+3 \label{eq:xdef} \end{equation} In equation (\ref{eq:xdef}) we saw $\dots$
\begin{equation} \begin{array}{l} \displaystyle \int 1 = x + C\\ \displaystyle \int x = \frac{x^2}{2} + C \\ \displaystyle \int x^2 = \frac{x^3}{3} + C \end{array} \label{eq:xdef} \end{equation}
\begin{eqnarray} && \int 1 = x + C \nonumber\\ && \int x = \frac{x^2}{2} + C \nonumber\\ && \int x^2 = \frac{x^3}{3} + C \label{eq:xdef} \end{eqnarray}

Braces

$\left] 0,1 \right[ + \lceil x \rfloor - \langle x,y\rangle$
$$ {n+1\choose k} = {n\choose k} + {n \choose k-1} $$
$$ |x| = \left\{ \begin{array}{rl} -x &\mbox{ if $x<0$}>
$$ F(x,y)=0 ~~\mbox{and}~~ \left| \begin{array}{ccc} F''_{xx} & F''_{xy} & F'_x \\ F''_{yx} & F''_{yy} & F'_y \\ F'_x & F'_y & 0 \end{array}\right| = 0 $$
$$ \underbrace{n(n-1)(n-2)\dots(n-m+1)}_ {\mbox{total of $m$ factors}} $$

Accents

Accents in text mode: gar\c con \'\i{} i t\`o\'s\.g\^o na\"\i ve na\"ive Ha\v cek \r Angstr\"om
Accents in math mode: $\hat{x}$, $\check{x}$, $\tilde{a}$, $\bar{\ell}$, $\dot{y}$, $\ddot{y}$, $\vec{z_1}$, $\vec{z}_1$
Wide accents, under and overline: $\hat{T} = \widehat{T}$, $\bar{T} = \overline{T}$, $\widetilde{xyz}$, $\overbrace{a+\underbrace{b+c}+d}$
$$ \overline{\overline{a}^2+\underline{xy} +\overline{\overline{z}}} $$
Sub and superscripts to braces: $$ \underbrace{a+\overbrace{b+\cdots}^{{}=t}+z} _{\mathrm{total}} ~~ a+{\overbrace{b+\cdots}}^{126}+z $$