Help:LaTeX Symbol Tables - Mathematics

Arrows
$$\gets \to \swarrow$$


 * 1) Accents
 * 2) Arrows
 * 3) Binary and relational operators
 * 4) Delimiters
 * 5) Greek letters
 * 6) Miscellaneous symbols
 * 7) Math functions
 * 8) Variable size math symbols
 * 9) Math Miscellany

The AMS dot symbols are named according to their intended usage: \dotsb between pairs of binary operators/relations, \dotsc between pairs of commas, \dotsi between pairs of integrals, \dotsm between pairs of multiplication signs, and \dotso between other symbol pairs.

Fractions, matrices, multilines
$$\frac{2}{4}=0.5$$

Small Fractions $$\tfrac{2}{4} = 0.5$$

Large (normal) Fractions $$\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a$$

Large (nested) Fractions $$\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a$$

Binomial coefficients $$\binom{n}{k}$$

Small Binomial coefficients $$\tbinom{n}{k}$$

Large (normal) Binomial coefficients $$\dbinom{n}{k}$$

Matrices \begin{matrix} x & y \\ z & v \end{matrix} $$\begin{matrix} x & y \\ z & v \end{matrix}$$

\begin{vmatrix} x & y \\ z & v \end{vmatrix} $$\begin{vmatrix} x & y \\ z & v \end{vmatrix}$$

\begin{Vmatrix} x & y \\ z & v \end{Vmatrix} $$\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$$

\begin{bmatrix} 0     & \cdots & 0      \\ \vdots & \ddots & \vdots \\ 0     & \cdots & 0 \end{bmatrix} $$\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} $$

\begin{Bmatrix} x & y \\ z & v \end{Bmatrix} $$\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$$

\begin{pmatrix} x & y \\ z & v \end{pmatrix} $$\begin{pmatrix} x & y \\ z & v \end{pmatrix}$$

\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) $$ \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) $$

Case distinctions f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} $$f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} $$

Multiline equations \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} $$ \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} $$

\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} $$ \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} $$ Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed)  \begin{array}{lcl}  z        & = & a \\  f(x,y,z) & = & x + y + z  \end{array}   $$\begin{array}{lcl}  z        & = & a \\  f(x,y,z) & = & x + y + z  \end{array}$$

Multiline equations (more) \begin{array}{lcr} z       & = & a \\ f(x,y,z) & = & x + y + z    \end{array} $$\begin{array}{lcr} z       & = & a \\ f(x,y,z) & = & x + y + z    \end{array}$$

Breaking up a long expression so that it wraps when necessary $$f(x) \,\!$$ $$= \sum_{n=0}^\infty a_n x^n $$ $$= a_0+a_1x+a_2x^2+\cdots$$ $$f(x) \,\!$$$$= \sum_{n=0}^\infty a_n x^n $$$$= a_0 +a_1x+a_2x^2+\cdots$$

Simultaneous equations \begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases} $$\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}$$

Arrays \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} $$ \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} $$

Parenthesizing big expressions, brackets, bars
You can use various delimiters with \left and \right:

Alphabets and typefaces
Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.

Color
Equations can use color:


 * $${\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}$$
 * $${\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}$$


 * $$x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}$$
 * $$x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}$$

See here for all named colors supported by LaTeX.

Note that color should not be used as the only way to identify something, because it will become meaningless on black-and-white media or for color-blind people. See en:Wikipedia:Manual of Style.

Spacing
Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Alignment with normal text flow
Due to the default css

img.tex { vertical-align: middle; }

an inline expression like $$\int_{-N}^{N} e^x\, dx$$ should look good.

If you need to align it otherwise, use  and play with the   argument until you get it right; however, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

Examples
A sample conforming diagram is.

Quadratic Polynomial
$$ax^2 + bx + c = 0$$ $$ax^2 + bx + c = 0$$

Quadratic Polynomial (Force PNG Rendering)
$$ax^2 + bx + c = 0\,\!$$ $$ax^2 + bx + c = 0\,\!$$

Quadratic Formula
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Tall Parentheses and Fractions
$$2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)$$ $$2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)$$

$$S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}$$ $$S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}$$

Integrals
$$\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy$$ $$\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy$$

Summation
$$\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}$$ $$\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}$$

Differential Equation
$$u'' + p(x)u' + q(x)u=f(x),\quad x>a$$ $$u'' + p(x)u' + q(x)u=f(x),\quad x>a$$

Complex numbers
$$|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)$$ $$|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)$$

Limits
$$\lim_{z\rightarrow z_0} f(z)=f(z_0)$$ $$\lim_{z\rightarrow z_0} f(z)=f(z_0)$$

Integral Equation
$$\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R}  \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR$$ $$\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR$$

Example
$$\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}$$ $$\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}$$

Continuation and cases
$$f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \mbox{otherwise}\end{cases}$$ $$ f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \mbox{otherwise} \end{cases} $$

Prefixed subscript
$${}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}$$ $${}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n} \frac{z^n}{n!}$$

Fraction and small fraction
$$ \frac {a}{b}$$ &emsp; $$ \tfrac {a}{b} $$ $$ \frac {a}{b}\ \tfrac {a}{b} $$

Table 40: Binary Operators
* '''Not predefined in $$\mathrm{L\!\!^{{}_{\scriptstyle A}} \!\!\!\!\!\;\; T\!_{\displaystyle E} \! X} \, 2_{\displaystyle \varepsilon}$$. One of the packages latexsym, amsfonts, amssymb, txfonts, pxfonts, or wasysym is required.'''

Table 157: Extensible Accents
* The yhmath package is required.

Table 163 mathabx Extensible Accents
The braces shown for \overbrace and \underbrace appear in their minimum size. They can expand arbitrarily wide, however.

Table 164: esvect Extensible Accents
esvect also defines a \vv* macro which is used to typeset arrows over vector variables with subscripts.

Table 174: Dots
* While “:” is valid in math mode, \colon uses different surrounding spacing.