This document mainly copied the content from this link to study the LaTex for mathmatic equation.
Reserved Symbol
There are some characters which need to be typed out by a specific method in LaTex.
| Symbol |
LaTex |
Symbol |
LaTex |
| # |
\# |
{ |
\{ |
| % |
\% |
} |
\} |
| ^ |
^\wedge |
~ |
\sim |
| & |
\& |
\ |
\backslash |
| _ |
\_ |
|
|
Greek Alphabet
| Symbol |
LaTeX |
Capitalize |
LaTeX |
With var prefix |
LaTeX |
Phonetic Symbol |
| $\alpha$ |
\alpha |
|
|
|
|
/’ælfə/ |
| $\beta$ |
\beta |
|
|
|
|
/’beɪtə/ |
| $\gamma$ |
\gamma |
$\Gamma$ |
\Gamma |
$\varGamma$ |
\varGamma |
/’ɡæmə/ |
| $\delta$ |
\delta |
$\Delta$ |
\Delta |
$\varDelta$ |
\varDelta |
/’dɛltə/ |
| $\epsilon$ |
\epsilon |
|
|
|
|
/’ɛpsɪlɒn/ |
| $\zeta$ |
\zeta |
|
|
|
|
/’zeɪtə/ |
| $\eta$ |
\eta |
|
|
|
|
/’eɪtə/ |
| $\theta$ |
\theta |
$\Theta$ |
\Theta |
$\varTheta,\vartheta$ |
\varTheta,\vartheta |
/’θiːtə/ |
| $\iota$ |
\iota |
|
|
|
|
/aɪ’oʊtə/ |
| $\kappa$ |
\kappa |
|
|
$\varkappa$ |
\varkappa |
/’kæpə/ |
| $\lambda$ |
\lambda |
$\Lambda$ |
\Lambda |
$\varLambda$ |
\varLambda |
/’læmdə/ |
| $\mu$ |
\mu |
|
|
|
|
/mjuː/ |
| $\nu$ |
\nu |
|
|
|
|
/njuː/ |
| $\xi$ |
\xi |
$\Xi$ |
\Xi |
$\varXi$ |
\varXi |
/zaɪ,ksaɪ/ |
| $o$ |
o |
$O$ |
O |
|
|
/’ɒmɪkrɒn/ |
| $\pi$ |
\pi |
$\Pi$ |
\Pi |
$\varPi,\varpi$ |
\varPi,\varpi |
/paɪ/ |
| $\rho$ |
\rho |
|
|
$\varrho$ |
\varrho |
/roʊ/ |
| $\sigma$ |
\sigma |
$\Sigma$ |
\Sigma |
$\varSigma,\varsigma$ |
\varSigma,\varsigma |
/ˈsɪɡmə/ |
| $\tau$ |
\tau |
|
|
|
|
/taʊ,tɔː/ |
| $\upsilon$ |
\upsilon |
$\Upsilon$ |
\Upsilon |
$\varUpsilon$ |
\varUpsilon |
/ˈʌpsɪlɒn/ |
| $\phi$ |
\phi |
$\Phi$ |
\Phi |
$\varPhi,\varphi$ |
\varPhi,\varphi |
/faɪ/ |
| $\chi$ |
\chi |
|
|
|
|
/kaɪ/ |
| $\psi$ |
\psi |
$\Psi$ |
\Psi |
$\varPsi$ |
\varPsi |
/psaɪ/ |
| $\omega$ |
\omega |
$\Omega$ |
\Omega |
$\varOmega$ |
\varOmega |
/oʊˈmeɪɡə/ |
| $\digamma$ |
\digamma |
|
|
|
|
/daɪ’gæmə/ |
Hebrew Alphabet
| Symbol |
LaTex |
English |
| $\aleph$ |
\aleph |
aleph |
| $\beth$ |
\beth |
beth |
| $\gimel$ |
\gimel |
gimel |
| $\daleth$ |
\daleth |
daleth |
Symbols
| Symbol |
LaTex |
Symbol |
LaTex |
| $\times$ |
\times |
$\div$ |
\div |
| $\pm$ |
\pm |
$\mp$ |
\mp |
| $\triangleleft$ |
\triangleleft |
$\triangleright$ |
\triangleright |
| $\cdot$ |
\cdot |
$\setminus$ |
\setminus |
| $\infty$ |
\infty |
$\circledS$ |
\circledS |
| $\star$ |
\star |
$\ast$ |
\ast |
| $\cup$ |
\cup |
$\cap$ |
\cap |
| $\sqcup$ |
\sqcup |
$\sqcap$ |
\sqcap |
| $\vee$ |
\vee |
$\wedge$ |
\wedge |
| $\circ$ |
\circ |
$\bullet$ |
\bullet |
| $\oplus$ |
\oplus |
$\ominus$ |
\ominus |
| $\odot$ |
\odot |
$\odot$ |
\odot |
| $\oslash$ |
\oslash |
$\oslash$ |
\oslash |
| $\otimes$ |
\otimes |
$\bigcirc$ |
\bigcirc |
| $\diamond$ |
\diamond |
$\uplus$ |
\uplus |
| $\bigtriangleup$ |
\bigtriangleup |
$\bigtriangledown$ |
\bigtriangledown |
| $\lhd$ |
\lhd |
$\rhd$ |
\rhd |
| $\unlhd$ |
\unlhd |
$\unrhd$ |
\unrhd |
| $\amalg$ |
\amalg |
$\wr$ |
\wr |
| $\dagger$ |
\dagger |
$\ddagger$ |
\ddagger |
| $\ne$ |
\ne,\neq |
$\equiv$ |
\equiv |
| $\not\equiv$ |
\not\equiv |
$\doteq$ |
\doteq |
| $\doteqdot$ |
\doteqdot |
$\overset{\underset{\mathrm{def}}{}}{=}$ |
\overset{\underset{\mathrm{def}}{}}{=} |
| $\sim$ |
\sim |
$\nsim$ |
\nsim |
| $\backsim$ |
\backsim |
$\thicksim$ |
\thicksim |
| $\simeq$ |
\simeq |
$\backsimeq$ |
\backsimeq |
| $\eqsim$ |
\eqsim |
$\cong$ |
\cong |
| $\ncong$ |
\ncong |
$\approx$ |
\approx |
| $\thickapprox$ |
\thickapprox |
$\approxeq$ |
\approxeq |
| $\asymp$ |
\asymp |
$\propto$ |
\propto |
| $\varpropto$ |
\varpropto |
$\nless$ |
\nless |
| $\ll$ |
\ll |
$\not\ll$ |
\not\ll |
| $\lll$ |
\lll |
$\not\lll$ |
\not\lll |
| $\lessdot$ |
\lessdot |
$\ngtr$ |
\ngtr |
| $\gg$ |
\gg |
$\not\gg$ |
\not\gg |
| $\ggg$ |
\ggg |
$\not\ggg$ |
\not\ggg |
| $\gtrdot$ |
\gtrdot |
$\le$ |
\le |
| $\leq$ |
\leq |
$\lneq$ |
\lneq |
| $\leqq$ |
\leqq |
$\nleq$ |
\nleq |
| $\nleqq$ |
\nleqq |
$\lneqq$ |
\lneqq |
| $\lvertneqq$ |
\lvertneqq |
$\ge$ |
\ge |
| $\geq$ |
\geq |
$\gneq$ |
\gneq |
| $\geqq$ |
\geqq |
$\ngeq$ |
\ngeq |
| $\ngeqq$ |
\ngeqq |
$\gneqq$ |
\gneqq |
| $\gvertneqq$ |
\gvertneqq |
$\lessgtr$ |
\lessgtr |
| $\lesseqgtr$ |
\lesseqgtr |
$\lesseqqgtr$ |
\lesseqqgtr |
| $\gtrless$ |
\gtrless |
$\gtreqless$ |
\gtreqless |
| $\gtreqqless$ |
\gtreqqless |
$\leqslant$ |
\leqslant |
| $\nleqslant$ |
\nleqslant |
$\eqslantless$ |
\eqslantless |
| $\geqslant$ |
\geqslant |
$\ngeqslant$ |
\ngeqslant |
| $\eqslantgtr$ |
\eqslantgtr |
$\lesssim$ |
\lesssim |
| $\exists$ |
\exists |
$\forall$ |
\forall |
| $\because$ |
\because |
$\therefore$ |
\therefore |
| $\And$ |
\And |
$\in$ |
\in |
| $\notin$ |
notin |
$\ni$ |
\ni |
| $\subseteq$ |
\subseteq |
$\supseteq$ |
\supseteq |
| $\nsubseteq$ |
\nsubseteq |
$\Rightarrow$ |
\Rightarrow |
| $\leftarrow$ |
\leftarrow |
$\iff$ |
\iff |
Geometric Symbol
| Symbol |
LaTex |
Symbol |
LaTex |
| $\parallel$ |
\parallel |
$\nparallel$ |
\nparallel |
| $\shortparallel$ |
\shortparallel |
$\nshortparallel$ |
\nshortparallel |
| $\perp$ |
\perp |
$\angle$ |
\angle |
| $\sphericalangle$ |
\sphericalangle |
$\measuredangle$ |
\measuredangle |
| $45^\circ$ |
\45^\circ |
$\bigstar$ |
\bigstar |
| $\Box$ |
\Box |
$\blacksquare$ |
\blacksquare |
| $\diamond$ |
\diamond |
$\lozenge$ |
\lozenge,\Diamond |
| $\blacklozenge$ |
\blacklozenge |
$\bigcirc$ |
\bigcirc |
| $\triangle$ |
\triangle,bigtriangleup |
$\bigtriangledown$ |
\bigtriangledown |
| $\vartriangle$ |
\vartriangle |
$\triangledown$ |
\triangledown |
| $\blacktriangle$ |
\blacktriangle |
$\blacktriangledown$ |
\blacktriangledown |
| $\blacktriangleleft$ |
\blacktriangleleft |
$\blacktriangleright$ |
\blacktriangleright |
Symbols on letter/number
| Symbol |
LaTex |
Symbol |
LaTex |
| $\bar{q}$ |
\bar{q} |
$\bar{abc}$ |
\bar{abc} |
| $\overline{q}$ |
\overline{q} |
$\overline{abc}$ |
\overline{abc} |
| $\not\operatorname{R}$ |
\not\operatorname{R} |
$\overset{\frown} {AB}$ |
\overset{\frown} {AB} |
| $\dot{x}$ |
\dot{x} |
$\ddot{x}$ |
\ddot{x} |
| $\overbrace{ 1+2+\cdots+100 }^{5050}$ |
\overbrace{ 1+2+\cdots+100 }^{5050} |
|
|
| $\underbrace{ a+b+\cdots+z }_{26}$ |
\underbrace{ a+b+\cdots+z }_{26} |
|
|
Space
The distance of a space is defined as em, and the actual size of em is changing with the font size.
| Size |
Example |
LaTex |
Double em |
$a \qquad b$ |
a \qquad b |
Single em |
$a \quad b$ |
a \quad b |
1/3 em |
$a\ b$ |
a\ b |
2/7 em |
$a\;b$ |
a\;b |
1/6 em |
$a\,b$ |
a\,b |
| No Space |
$ab$ |
ab |
Fraction
| Example |
Latex |
| $\frac{2}{4}x=0.5x\ or\ {2 \over 4}x=0.5x$ |
\frac{2}{4}x=0.5x\ or\ {2 \over 4}x=0.5x |
| $\tfrac{2}{4}x = 0.5x$ |
\tfrac{2}{4}x = 0.5x |
| $\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a$ |
\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a |
| $\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a$ |
\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a |
Numerical Function
| Example |
Latex |
| $\exp_a b = a^b, \exp b = e^b, 10^m$ |
\exp_a b = a^b, \exp b = e^b, 10^m |
| $\ln c, \lg d = \log e, \log_{10} f$ |
\ln c, \lg d = \log e, \log_{10} f |
| $\sin a, \cos b, \tan c, \cot d, \sec e, \csc f$ |
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f |
| $\arcsin a, \arccos b, \arctan c$ |
\arcsin a, \arccos b, \arctan c |
| $\operatorname{arccot} d, \operatorname{arcsec} e, \operatorname{arccsc} f$ |
\operatorname{arccot} d, \operatorname{arcsec} e, \operatorname{arccsc} f |
| $\sinh a, \cosh b, \tanh c, \coth d$ |
\sinh a, \cosh b, \tanh c, \coth d |
| $\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n$ |
\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n |
| $\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q$ |
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q |
| $\operatorname{sgn}r, \left\vert s \right\vert$ |
\operatorname{sgn}r, \left\vert s \right\vert |
| $\min(x,y), \max(x,y)$ |
\min(x,y), \max(x,y) |
LaTex also allow user customizing special function style by \operatorname{}
| Example |
Latex |
| $\operatorname{mydefine}x$ |
\operatorname{mydefine}x |
$n^{th}$ Root
| Symbol |
LaTex |
Symbol |
LaTex |
| $\surd$ |
\surd |
$\sqrt{\pi}$ |
\sqrt{\pi} |
| $\sqrt[n]{\pi}$ |
\sqrt[n]{\pi} |
$\sqrt[3]{\frac{x^3+y^3}{2}}$ |
\sqrt[3]{\frac{x^3+y^3}{2}} |
Differentiation & Derivatives
| Symbol |
LaTex |
| $dt, \mathrm{d}t, \partial t, \nabla\psi$ |
dt, \mathrm{d}t, \partial t, \nabla\psi |
| $dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y$ |
dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y |
| $\prime, \backprime, f^\prime, f’, f’’, f^{(3)}, \dot y, \ddot y$ |
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y |
Modulo Operation
| Symbol |
LaTex |
| $s_k \equiv 0 \pmod{m}$ |
s_k \equiv 0 \pmod{m} |
| $a \bmod b$ |
a \bmod b |
| $\gcd(m, n), \operatorname{lcm}(m, n)$ |
\gcd(m, n), \operatorname{lcm}(m, n) |
| $\mid, \nmid, \shortmid, \nshortmid$ |
\mid, \nmid, \shortmid, \nshortmid |
Limit
| Symbol |
LaTex |
| $\lim_{n \to \infty}x_n$ |
\lim_{n \to \infty}x_n |
| $\textstyle \lim_{n \to \infty}x_n$ |
\textstyle \lim_{n \to \infty}x_n |
Range & Prediction
| Symbol |
LaTex |
| $\min x, \max y, \inf s, \sup t$ |
\min x, \max y, \inf s, \sup t |
| $\lim u, \liminf v, \limsup w$ |
\lim u, \liminf v, \limsup w |
| $\dim p, \deg q, \det m, \ker\phi$ |
\dim p, \deg q, \det m, \ker\phi |
| $\Pr j, \hom l, \lVert z \rVert, \arg z$ |
\Pr j, \hom l, \lVert z \rVert, \arg z |
Integral
| Example |
LaTex |
| $\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx$ |
\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx |
| $\int_{1}^{3}\frac{e^3/x}{x^2}\, dx$ |
\int_{1}^{3}\frac{e^3/x}{x^2}\, dx |
| $\textstyle \int\limits_{-N}^{N} e^x dx$ |
\textstyle \int\limits_{-N}^{N} e^x dx |
| $\textstyle \int_{-N}^{N} e^x dx$ |
\textstyle \int_{-N}^{N} e^x dx |
| $\iint\limits_D dx\,dy$ |
\iint\limits_D dx\,dy |
| $\iiint\limits_E dx\,dy\,dz$ |
\iiint\limits_E dx\,dy\,dz |
| $\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy$ |
\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy |
| $\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy$ |
\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy |
\int\_{}^{} is used for single integral, double integral is \iint\_{}^{}, and so on, until quadruple integral.
Calculation Symbol
| Type |
Symbol |
LaTex |
| Product |
$\prod_{a}^{b}$ |
\prod_{a}^{b} |
| Coproduct |
$\coprod_{a}^{b}$ |
\coprod_{a}^{b} |
| Union |
$\bigcup_{a}^{b}$ |
\bigcup_{a}^{b} |
| Intersection |
$\bigcap_{a}^{b}$ |
\bigcap_{a}^{b} |
| Disjunctive |
$\bigvee_{a}^{b}$ |
\bigvee_{a}^{b} |
| Conjunction |
$\bigwedge_{a}^{b}$ |
\bigwedge_{a}^{b} |
| Sum |
$\sum_{a}^{b}$ |
\sum_{a}^{b} |
Binomial
| Type |
Example |
LaTex |
| Binomial Cofficient |
$\binom{n}{k}$ |
\binom{n}{k} |
| Smaller Binomial Cofficient |
$\tbinom{n}{k}$ |
\tbinom{n}{k} |
| Larger Binomial Cofficient |
$\dbinom{n}{k}$ |
\dbinom{n}{k} |
Matrix
| Example |
LaTex |
| \(\begin{matrix}x & y \\ z & v\end{matrix}\) |
\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) |
Array
\[\begin{array}{ | c | c | c | }
a & b & S \\
\hline
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{array}\]
LaTex:
\begin{array}{ | c | c | c | }
a & b & S \\
\hline
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0
\end{array}
Equation Sets
Without Condition
\[\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}\]
LaTex:
\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
With Condition
\[f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}\]
Latex:
f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}
Multi-line Equation
\[\begin{align}
f(x) & = (a+b)^2\\
& = a^2+2ab+b^2
\end{align}\]
LaTex:
\begin{align}
f(x) & = (a+b)^2\\
& = a^2+2ab+b^2
\end{align}
Letter Style
| Type |
Example |
LaTex |
| Normal |
$Ab9$ |
Ab9 |
| Script |
$\mathcal{Ab9}$ |
\mathcal{Ab9} |
| Blackboard |
$\mathbb{Ab9}$ |
\mathbb{Ab9} |
| Bold |
$\boldsymbol{Ab9}$ |
\boldsymbol{Ab9} |
| Italic |
$\mathit{Ab9}$ |
\mathit{Ab9} |
| Roman |
$\mathrm{Ab9}$ |
\mathrm{Ab9} |
