Latex QuickNote | Longsen Gao

Universal LaTeX Math Formula Syntax Manual

MathJax is an open source JavaScript mathematical sign rendering engine that runs in Web browsers, making it easy to display mathematical formulas in modern Web browsers, and is currently capable of parsing markup languages such as LaTex and MathML. languages such as LaTex and MathML. The MathJax project originated in 2009 and is currently hosted by the NumFOCUS Foundation and supported by the MathJax Consortium, a joint venture of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM).

LaTeX is a high-quality typesetting format for generating complex tables and mathematical formulas, and is currently the de facto standard in the electronic and mathematical publishing industry. This article summarizes the LaTeX syntax often used in writing mathematical formulas, using Pandoc as the LaTex rendering engine (a command-line tool for markup language document conversion), so that you can easily refer to it when writing related scientific and technical articles.

Reserved Character

Reserved characters with special meanings in the LaTeX environment cannot be used directly, but must be realized by the specified syntax:

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$#$	`\#`	6	${$	`\{`
2	$%$	`\%`	7	$}$	`\}`
3	$^{\land}$	`^\wedge`	8	$\sim$	`\sim`
4	$&$	`\&`	9	$∖$	`\backslash`
5	$_$	`\_`

Greek Alphabet

No.	Sign	LaTeX	Uppercase letters	LaTeX	Use `var` as prefix	LaTeX	pronun.
1	$α$	`\alpha`					/ˈælfə/
2	$β$	`\beta`					/ˈbeɪtə/
3	$γ$	`\gamma`	$Γ$	`\Gamma`	$Γ$	`\varGamma`	/ˈɡæmə/
4	$δ$	`\delta`	$Δ$	`\Delta`	$Δ$	`\varDelta`	/ˈdɛltə/
5	$ϵ$	`\epsilon`			$ε$	`\varepsilon`	/ˈɛpsɪlɒn/
6	$ζ$	`\zeta`					/ˈzeɪtə/
7	$η$	`\eta`					/ˈeɪtə/
8	$θ$	`\theta`	$Θ$	`\Theta`	$ϑ$ 、 $Θ$	`\vartheta`、`\varTheta`	/ˈθiːtə/
9	$ι$	`\iota`					/aɪˈoʊtə/
10	$κ$	`\kappa`			$ϰ$	`\varkappa`	/ˈkæpə/
11	$λ$	`\lambda`	$Λ$	`\Lambda`	$Λ$	`\varLambda`	/ˈlæmdə/
12	$μ$	`\mu`					/mjuː/
13	$ν$	`\nu`					/njuː/
14	$ξ$	`\xi`	$Ξ$	`\Xi`	$Ξ$	`\varXi`	/zaɪ, ksaɪ/
15	$o$	`o`	$O$	`O`			/ˈɒmɪkrɒn/
16	$π$	`\pi`	$Π$	`\Pi`	$ϖ$ 、 $Π$	`\varpi`、`\varPi`	/paɪ/
17	$ρ$	`\rho`			$ϱ$	`\varrho`	/roʊ/
18	$σ$	`\sigma`	$Σ$	`\Sigma`	$ς$ 、 $Σ$	`\varsigma`、`\varSigma`	/ˈsɪɡmə/
19	$τ$	`\tau`					/taʊ, tɔː/
20	$υ$	`\upsilon`	$Υ$	`\Upsilon`	$Υ$	`\varUpsilon`	/ˈʌpsɪlɒn/
21	$ϕ$	`\phi`	$Φ$	`\Phi`	$φ$ 、 $Φ$	`\varphi`、`\varPhi`	/faɪ/
22	$χ$	`\chi`					/kaɪ/
23	$ψ$	`\psi`	$Ψ$	`\Psi`	$Ψ$	`\varPsi`	/psaɪ/
24	$ω$	`\omega`	$Ω$	`\Omega`	$Ω$	`\varOmega`	/oʊˈmeɪɡə/
25	$ϝ$	`\digamma`					/daɪ’gæmə/

Hebrew alphabet

No.	Sign	LaTeX	English	No.	Sign	LaTeX	English
1	$ℵ$	`\aleph`	aleph	3	$ℷ$	`\gimel`	gimel
2	$ℶ$	`\beth`	beth	4	$ℸ$	`\daleth`	daleth

Binary Operator

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$+$	`+`	20	$∙$	`\bullet`
2	$-$	`-`	21	$\oplus$	`\oplus`
3	$\times$	`\times`	22	$⊖$	`\ominus`
4	$\div$	`\div`	23	$⊙$	`\odot`
5	$\pm$	`\pm`	24	$⊘$	`\oslash`
6	$\mp$	`\mp`	25	$\otimes$	`\otimes`
7	$◃$	`\triangleleft`	26	$◯$	`\bigcirc`
8	$▹$	`\triangleright`	27	$⋄$	`\diamond`
9	$\cdot$	`\cdot`	28	$⊎$	`\uplus`
10	$∖$	`\setminus`	29	$△$	`\bigtriangleup`
11	$⋆$	`\star`	30	$▽$	`\bigtriangledown`
12	$*$	`\ast`	31	$⊲$	`\lhd`
13	$\cup$	`\cup`	32	$⊳$	`\rhd`
14	$\cap$	`\cap`	33	$⊴$	`\unlhd`
15	$⊔$	`\sqcup`	34	$⊵$	`\unrhd`
16	$⊓$	`\sqcap`	35	$⨿$	`\amalg`
17	$\lor$	`\vee`	36	$≀$	`\wr`
18	$\land$	`\wedge`	37	$†$	`\dagger`
19	$\circ$	`\circ`	38	$‡$	`\ddagger`

Binary Relation Symbol

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$=$	`=`	49	$⪈$	`\gneq`
2	$\neq$	`\ne`	50	$≧$	`\geqq`
3	$\neq$	`\neq`	51	$≱$	`\ngeq`
4	$\equiv$	`\equiv`	52	$≱$	`\ngeqq`
5	$≢$	`\not\equiv`	53	$≩$	`\gneqq`
6	$≐$	`\doteq`	54	$≩$	`\gvertneqq`
7	$≑$	`\doteqdot`	55	$≶$	`\lessgtr`
8	$\overset{\underset{def}{}}{=}$	`\overset{\underset{\mathrm{def}}{}}{=}`	56	$⋚$	`\lesseqgtr`
9	$:=$	`:=`	57	$⪋$	`\lesseqqgtr`
10	$\sim$	`\sim`	58	$≷$	`\gtrless`
11	$≁$	`\nsim`	59	$⋛$	`\gtreqless`
12	$∽$	`\backsim`	60	$⪌$	`\gtreqqless`
13	$\sim$	`\thicksim`	61	$⩽$	`\leqslant`
14	$≃$	`\simeq`	62	$⪇$	`\nleqslant`
15	$⋍$	`\backsimeq`	63	$⪕$	`\eqslantless`
16	$≂$	`\eqsim`	64	$⩾$	`\geqslant`
17	$≅$	`\cong`	65	$⪈$	`\ngeqslant`
18	$≇$	`\ncong`	66	$⪖$	`\eqslantgtr`
19	$\approx$	`\approx`	67	$≲$	`\lesssim`
20	$\approx$	`\thickapprox`	68	$⋦$	`\lnsim`
21	$≊$	`\approxeq`	69	$⪅$	`\lessapprox`
22	$≍$	`\asymp`	70	$⪉$	`\lnapprox`
23	$\propto$	`\propto`	71	$≳$	`\gtrsim`
24	$\propto$	`\varpropto`	72	$⋧$	`\gnsim`
25	$<$	`<`	73	$⪆$	`\gtrapprox`
26	$≮$	`\nless`	74	$⪊$	`\gnapprox`
27	$≪$	`\ll`	75	$≺$	`\prec`
28	$≪̸$	`\not\ll`	76	$⊀$	`\nprec`
29	$⋘$	`\lll`	77	$⪯$	`\preceq`
30	$⋘̸$	`\not\lll`	78	$⋠$	`\npreceq`
31	$⋖$	`\lessdot`	79	$⪵$	`\precneqq`
32	$>$	`>`	80	$≻$	`\succ`
33	$≯$	`\ngtr`	81	$⊁$	`\nsucc`
34	$≫$	`\gg`	82	$⪰$	`\succeq`
35	$≫̸$	`\not\gg`	83	$⋡$	`\nsucceq`
36	$⋙$	`\ggg`	84	$⪶$	`\succneqq`
37	$⋙̸$	`\not\ggg`	85	$≼$	`\preccurlyeq`
38	$⋗$	`\gtrdot`	86	$⋞$	`\curlyeqprec`
39	$\leq$	`\le`	87	$≽$	`\succcurlyeq`
40	$\leq$	`\leq`	88	$⋟$	`\curlyeqsucc`
41	$⪇$	`\lneq`	89	$≾$	`\precsim`
42	$≦$	`\leqq`	90	$⋨$	`\precnsim`
43	$≰$	`\nleq`	91	$⪷$	`\precapprox`
44	$≰$	`\nleqq`	92	$⪹$	`\precnapprox`
45	$≨$	`\lneqq`	93	$≿$	`\succsim`
46	$≨$	`\lvertneqq`	94	$⋩$	`\succnsim`
47	$\geq$	`\ge`	95	$⪸$	`\succapprox`
48	$\geq$	`\geq`	96	$⪺$	`\succnapprox`

Geometric Sign

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$∥$	`\parallel`	14	$◊$	`\lozenge`
2	$∦$	`\nparallel`	15	$⧫$	`\blacklozenge`
3	$∥$	`\shortparallel`	16	$★$	`\bigstar`
4	$∦$	`\nshortparallel`	17	$◯$	`\bigcirc`
5	$⊥$	`\perp`	18	$△$	`\triangle`
6	$∠$	`\angle`	19	$△$	`\bigtriangleup`
7	$∢$	`\sphericalangle`	20	$▽$	`\bigtriangledown`
8	$∡$	`\measuredangle`	21	$△$	`\vartriangle`
9	$45^{\circ}$	`45^\circ`	22	$▽$	`\triangledown`
10	$◻$	`\Box`	23	$▴$	`\blacktriangle`
11	$◼$	`\blacksquare`	24	$▾$	`\blacktriangledown`
12	$⋄$	`\diamond`	25	$◂$	`\blacktriangleleft`
13	$◊ ◊$	`\Diamond \lozenge`	26	$▸$	`\blacktriangleright`

Logic Sign

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$\forall$	`\forall`	20	$\neg$	`\neg`
2	$\exists$	`\exists`	21	$⧸ R$	`\not\operatorname{R}`
3	$∄$	`\nexists`	22	$⊥$	`\bot`
4	$∴$	`\therefore`	23	$⊤$	`\top`
5	$∵$	`\because`	24	$⊢$	`\vdash`
6	$&$	`\And`	25	$⊣$	`\dashv`
7	$\lor$	`\lor`	26	$⊨$	`\vDash`
8	$\lor$	`\vee`	27	$⊩$	`\Vdash`
9	$⋎$	`\curlyvee`	28	$⊨$	`\models`
10	$⋁$	`\bigvee`	29	$⊪$	`\Vvdash`
11	$\land$	`\land`	30	$⊬$	`\nvdash`
12	$\land$	`\wedge`	31	$⊮$	`\nVdash`
13	$⋏$	`\curlywedge`	32	$⊭$	`\nvDash`
14	$⋀$	`\bigwedge`	33	$⊯$	`\nVDash`
15	$\bar{q}$	`\bar{q}`	34	$⌜$	`\ulcorner`
16	$\bar{a b c}$	`\bar{abc}`	35	$⌝$	`\urcorner`
17	$\overset{―}{q}$	`\overline{q}`	36	$⌞$	`\llcorner`
18	$\overset{―}{a b c}$	`\overline{abc}`	37	$⌟$	`\lrcorner`
19	$\neg$	`\lnot`

Set Sign

No.	Sign	LaTeX	No.	Sign	LaTeX
1	${}$	`\{ \}`	23	$⊏$	`\sqsubset`
2	$\emptyset$	`\emptyset`	24	$\supset$	`\supset`
3	$\emptyset$	`\varnothing`	25	$⋑$	`\Supset`
4	$\in$	`\in`	26	$⊐$	`\sqsupset`
5	$\notin$	`\notin`	27	$\subseteq$	`\subseteq`
6	$∋$	`\ni`	28	$⊈$	`\nsubseteq`
7	$\cap$	`\cap`	29	$⊊$	`\subsetneq`
8	$⋒$	`\Cap`	30	$⊊$	`\varsubsetneq`
9	$⊓$	`\sqcap`	31	$⊑$	`\sqsubseteq`
10	$⋂$	`\bigcap`	32	$\supseteq$	`\supseteq`
11	$\cup$	`\cup`	33	$⊉$	`\nsupseteq`
12	$⋓$	`\Cup`	34	$⊋$	`\supsetneq`
13	$⊔$	`\sqcup`	35	$⊋$	`\varsupsetneq`
14	$⋃$	`\bigcup`	36	$⊒$	`\sqsupseteq`
15	$⨆$	`\bigsqcup`	37	$⫅$	`\subseteqq`
16	$⊎$	`\uplus`	38	$⊈$	`\nsubseteqq`
17	$⨄$	`\biguplus`	39	$⫋$	`\subsetneqq`
18	$∖$	`\setminus`	40	$⫋$	`\varsubsetneqq`
19	$∖$	`\smallsetminus`	41	$⫆$	`\supseteqq`
20	$\times$	`\times`	42	$⊉$	`\nsupseteqq`
21	$\subset$	`\subset`	43	$⫌$	`\supsetneqq`
22	$⋐$	`\Subset`	44	$⫌$	`\varsupsetneqq`

Arrow Sign

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$⇛$	`\Rrightarrow`	36	$⟼$	`\longmapsto`
2	$⇚$	`\Lleftarrow`	37	$⇀$	`\rightharpoonup`
3	$\Rightarrow$	`\Rightarrow`	38	$⇁$	`\rightharpoondown`
4	$⇏$	`\nRightarrow`	39	$↼$	`\leftharpoonup`
5	$⟹$	`\Longrightarrow`	40	$↽$	`\leftharpoondown`
6	$⟹$	`\implies`	41	$↿$	`\upharpoonleft`
7	$\Leftarrow$	`\Leftarrow`	42	$↾$	`\upharpoonright`
8	$⇍$	`\nLeftarrow`	43	$⇃$	`\downharpoonleft`
9	$⟸$	`\Longleftarrow`	44	$⇂$	`\downharpoonright`
10	$\Leftrightarrow$	`\Leftrightarrow`	45	$⇌$	`\rightleftharpoons`
11	$⇎$	`\nLeftrightarrow`	46	$⇋$	`\leftrightharpoons`
12	$⟺$	`\Longleftrightarrow`	47	$↶$	`\curvearrowleft`
13	$⟺$	`\iff`	48	$↺$	`\circlearrowleft`
14	$⇑$	`\Uparrow`	49	$↰$	`\Lsh`
15	$⇓$	`\Downarrow`	50	$⇈$	`\upuparrows`
16	$⇕$	`\Updownarrow`	51	$⇉$	`\rightrightarrows`
17	$\to$	`\rightarrow`	52	$⇄$	`\rightleftarrows`
18	$\to$	`\to`	53	$↣$	`\rightarrowtail`
19	$↛$	`\nrightarrow`	54	$↬$	`\looparrowright`
20	$⟶$	`\longrightarrow`	55	$↷$	`\curvearrowright`
21	$\leftarrow$	`\leftarrow`	56	$↻$	`\circlearrowright`
22	$\leftarrow$	`\gets`	57	$↱$	`\Rsh`
23	$↚$	`\nleftarrow`	58	$⇊$	`\downdownarrows`
24	$⟵$	`\longleftarrow`	59	$⇇$	`\leftleftarrows`
25	$\leftrightarrow$	`\leftrightarrow`	60	$⇆$	`\leftrightarrows`
26	$↮$	`\nleftrightarrow`	61	$↢$	`\leftarrowtail`
27	$⟷$	`\longleftrightarrow`	62	$↫$	`\looparrowleft`
28	$↑$	`\uparrow`	63	$↪$	`\hookrightarrow`
29	$↓$	`\downarrow`	64	$↩$	`\hookleftarrow`
30	$↕$	`\updownarrow`	65	$⊸$	`\multimap`
31	$↗$	`\nearrow`	66	$↭$	`\leftrightsquigarrow`
32	$↙$	`\swarrow`	67	$⇝$	`\rightsquigarrow`
33	$↖$	`\nwarrow`	68	$↠$	`\twoheadrightarrow`
34	$↘$	`\searrow`	69	$↞$	`\twoheadleftarrow`
35	$\mapsto$	`\mapsto`

Special Sign

No.	Sign	LaTeX	No.	Sign	LaTeX
1	$\infty$	`\infty`	33	$♭$	`\flat`
2	$ℵ$	`\aleph`	34	$♮$	`\natural`
3	$∁$	`\complement`	35	$♯$	`\sharp`
4	$∍$	`\backepsilon`	36	$╱$	`\diagup`
5	$ð$	`\eth`	37	$╲$	`\diagdown`
6	$Ⅎ$	`\Finv`	38	$\cdot$	`\centerdot`
7	$ℏ$	`\hbar`	39	$⋉$	`\ltimes`
8	$ℑ$	`\Im`	40	$⋊$	`\rtimes`
9	$ı$	`\imath`	41	$⋋$	`\leftthreetimes`
10	$ȷ$	`\jmath`	42	$⋌$	`\rightthreetimes`
11	$k$	`\Bbbk`	43	$≖$	`\eqcirc`
12	$ℓ$	`\ell`	44	$≗$	`\circeq`
13	$℧$	`\mho`	45	$≜$	`\triangleq`
14	$℘$	`\wp`	46	$≏$	`\bumpeq`
15	$ℜ$	`\Re`	47	$≎$	`\Bumpeq`
16	$Ⓢ$	`\circledS`	48	$≑$	`\doteqdot`
17	$⨿$	`\amalg`	49	$≓$	`\risingdotseq`
18	$%$	`\%`	50	$≒$	`\fallingdotseq`
19	$†$	`\dagger`	51	$⊺$	`\intercal`
20	$‡$	`\ddagger`	52	$⊼$	`\barwedge`
21	$\dots$	`\ldots`	53	$⊻$	`\veebar`
22	$\dots$	`\cdots`	54	$⩞$	`\doublebarwedge`
23	$⌣$	`\smile`	55	$≬$	`\between`
24	$⌢$	`\frown`	56	$⋔$	`\pitchfork`
25	$≀$	`\wr`	57	$⊲$	`\vartriangleleft`
26	$◃$	`\triangleleft`	58	$⋪$	`\ntriangleleft`
27	$▹$	`\triangleright`	59	$⊳$	`\vartriangleright`
28	$♢$	`\diamondsuit`	60	$⋫$	`\ntriangleright`
29	$♡$	`\heartsuit`	61	$⊴$	`\trianglelefteq`
30	$♣$	`\clubsuit`	62	$⋬$	`\ntrianglelefteq`
31	$♠$	`\spadesuit`	63	$⊵$	`\trianglerighteq`
32	$⅁$	`\Game`	64	$⋭$	`\ntrianglerighteq`

Points

Type	Sign	LaTeX
point	$\frac{2}{4} x = 0.5 x or \frac{2}{4} x = 0.5 x$	`\frac{2}{4}x=0.5x or {2 \over 4}x=0.5x`
small point	$\frac{2}{4} x = 0.5 x$	`\tfrac{2}{4}x = 0.5x`
big point (non-nested)	$\frac{2}{4} = 0.5 \frac{2}{c + \frac{2}{d + \frac{2}{4}}} = a$	`\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a`
big point （nested）	$\frac{2}{c + \frac{2}{d + \frac{2}{4}}} = a$	`\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a`

Numeric Function

Sign	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`
$arccot d, arcsec e, arccsc f$	`\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`
$sh k, ch l, th m, \coth n$	`\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n`
$argsh o, argch p, argth q$	`\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q`
$sgn r, \| s \|$	`\operatorname{sgn}r, \left\vert s \right\vert`
$min (x, y), max (x, y)$	`\min(x,y), \max(x,y)`

If a special function Sign is required, then it can be customized using the \operatorname{} command:

Sign	LaTeX
$mydefine x$	`\operatorname{mydefine}x`

Surd

Sign	LaTeX	Sign	LaTeX
$\sqrt$	`\surd`	$\sqrt[n]{π}$	`\sqrt[n]{\pi}`
$\sqrt{π}$	`\sqrt{\pi}`	$\sqrt[3]{\frac{x^{3} + y^{3}}{2}}$	`\sqrt[3]{\frac{x^3+y^3}{2}}*`_

Differentiation and Derivatives

Sign	LaTeX
$d t, d t, \partial t, \nabla ψ$	`dt, \mathrm{d}t, \partial t, \nabla\psi`
$d y / d x, d y / d x, \frac{d y}{d x}, \frac{d y}{d x}, \frac{\partial^{2}}{\partial x_{1} \partial x_{2}} y$	`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`
$', ‵, f^{'}, f^{'}, f^{″}, f^{(3)}, \dot{y}, \ddot{y}$	`\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y`

Sign	LaTeX
$s_{k} \equiv 0 (\mod m)$	`s_k \equiv 0 \pmod{m}`
$a mod b$	`a \bmod b`
$gcd (m, n), lcm (m, n)$	`\gcd(m, n), \operatorname{lcm}(m, n)`
$∣, ∤, ∣, ∤$	`\mid, \nmid, \shortmid, \nshortmid`

Limit

Sign	LaTeX
$lim_{n \to \infty} x_{n}$	`\lim_{n \to \infty}x_n`
$lim_{n \to \infty} x_{n}$	`\textstyle \lim_{n \to \infty}x_n`

Scope and Projections

Sign	LaTeX
$min x, max y, inf s, sup t$	`\min x, \max y, \inf s, \sup t`
$lim u, lim inf v, lim sup w$	`\lim u, \liminf v, \limsup w`
$\dim p, \deg q, det m, \ker ϕ$	`\dim p, \deg q, \det m, \ker\phi`
$Pr j, hom l, ‖ z ‖, \arg z$	`\Pr j, \hom l, \lVert z \rVert, \arg z`

Integral

Sign	LaTeX
$\int_{1}^{3} \frac{e^{3} / x}{x^{2}} d x$	`\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx`
$\int_{1}^{3} \frac{e^{3} / x}{x^{2}} d x$	`\int_{1}^{3}\frac{e^3/x}{x^2}\, dx`
$\int_{- N}^{N} e^{x} d x$	`\textstyle \int\limits_{-N}^{N} e^x dx`
$\int_{- N}^{N} e^{x} d x$	`\textstyle \int_{-N}^{N} e^x dx`
$\iint_{D} d x d y$	`\iint\limits_D dx\,dy`
$\underset{E}{∭} d x d y d z$	`\iiint\limits_E dx\,dy\,dz`
$\underset{F}{⨌} d x d y d z d t$	`\iiiint\limits_F dx\,dy\,dz\,dt`
$\int_{(x, y) \in C} x^{3} d x + 4 y^{2} d y$	`\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy`
$\oint_{(x, y) \in C} x^{3} d x + 4 y^{2} d y$	`\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy`

Note: Integral Sign is invoked by \int\_{}^{} command, Double Integral Sign is invoked by \iint\_{}^{}, and so on, up to four integrals can be supported.

Curve integrals can be invoked with the \oint command, but MathJax does not support this syntax, so it can be invoked with the \unicode{} command with the Unicode extension enabled:

Sign	LaTeX	Description
$∯ ∯_{C}$	`\unicode{8751} \unicode{x222F}_C`	The Unicode code for the surface integral Sign is `8751` in decimal and `x222F` in hexadecimal;
$∰ ∰_{C}$	`\unicode{8752} \unicode{x2230}_C`	The Unicode code for the 3D surface integral Sign is `8752` in decimal and `x2230` in hexadecimal;
$∱ ∱_{c} ∲ ∲_{c} ∳ ∳_{c}$	`\unicode{8753} \unicode{x2231}_c \unicode{8754} \unicode{x2232}_c \unicode{8755} \unicode{x2233}_c`	Other points Sign;

Large-scale Operators

Class	Sign	LaTeX	Sign	LaTeX
Summation	$\sum_{a}^{b}$	`\sum_{a}^{b}`	$\sum_{a}^{b}$	`\textstyle \sum_{a}^{b}`
coproduct	$\prod_{a}^{b}$	`\prod_{a}^{b}`	$\prod_{a}^{b}$	`\textstyle \prod_{a}^{b}`
residual product	$∐_{a}^{b}$	`\coprod_{a}^{b}`	$∐_{a}^{b}$	`\textstyle \coprod_{a}^{b}`
union	$⋃_{a}^{b}$	`\bigcup_{a}^{b}`	$⋃_{a}^{b}$	`\textstyle \bigcup_{a}^{b}`
intersection	$⋂_{a}^{b}$	`\bigcap_{a}^{b}`	$⋂_{a}^{b}$	`\textstyle \bigcap_{a}^{b}`
disjunction	$⋁_{a}^{b}$	`\bigvee_{a}^{b}`	$⋁_{a}^{b}$	`\textstyle \bigvee_{a}^{b}`
connective	$⋀_{a}^{b}$	`\bigwedge_{a}^{b}`	$⋀_{a}^{b}$	`\textstyle \bigwedge_{a}^{b}`

Superscript

Type	Sign	Code
superscript	$a^{2}$	`a^2`
	$a^{x + 3}$	`a^{x+3}`

suffix	$a_{2}$	`a_2`
combo	$10^{30} a^{2 + 2}$	`10^{30} a^{2+2}`
	$a i, j b f^{'}$	`a{i,j} b{f'}`

mix of upper and lower scales	$x_{2}^{3}$	`x_2^3`
	${x_{2}}^{3}$	`{x_2}^3`

superscript of superscript	$10^{10^{8}}$	`10^{10^{8}}`
hybrid logo	${1^{2} X 3^{4}}_{a}^{b}$	`\sideset{1^2}{3^4}X_a^b`
	$_{1}^{2}! Ω_{3}^{4}$	`{}_1^2!\Omega_3^4`

Top markups	$\overset{α}{ω}$	`\overset{\alpha}{\omega}`
	$\underset{α}{ω}$	`\underset{\alpha}{\omega}`
	$\overset{α}{\underset{γ}{ω}}$	`\overset{\alpha}{\underset{\gamma}{\omega}}`
	$\overset{α}{ω}$	`\stackrel{\alpha}{\omega}`



derivative	$x^{'}, y^{″}, f^{'}, f^{″}$ $x^{'}, y^{''}$	`x', y'', f', f''` `x^\prime, y^{\prime\prime}`
derivative point	$\dot{x}, \ddot{x}$	`\dot{x}, \ddot{x}`
Underline, upperline and Vector	$\hat{a} \bar{b} \vec{c}$	`\hat a \ \bar b \ \vec c`
	$\vec{a b} \overset{\leftarrow}{c d} \hat{d e f}$	`\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}`
	$\overset{―}{g h i} \underset{―}{j k l}$	`\overline{g h i} \ \underline{j k l}`


arc	$\overset{⌢}{A B}$	`\overset{\frown} {AB}`
arrow	$A \overset{n + μ - 1}{\leftarrow} B \to_{T}^{n \pm i - 1} C$	`A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C`
curly brackets	$\overset{5050}{\overset{⏞}{1 + 2 + \dots + 100}}$	`\overbrace{ 1+2+\cdots+100 }^{5050}`
bottom curly brackets	$\underset{26}{\underset{⏟}{a + b + \dots + z}}$	`\underbrace{ a+b+\cdots+z }_{26}`
sum calculus	$\sum_{k = 1}^{N} k^{2}$	`\sum_{k=1}^N k^2`
summation in text mode	$\sum_{k = 1}^{N} k^{2}$	`\textstyle \sum_{k=1}^N k^2`
summation in fractions	$\frac{\sum_{k = 1}^{N} k^{2}}{a}$	`\frac{\sum_{k=1}^N k^2}{a}`
summation in fractions	$\frac{\sum_{k = 1}^{N} k^{2}}{a}$	`\frac{\displaystyle \sum_{k=1}^N k^2}{a}`
summation in fractions	$\frac{\sum_{k = 1}^{^{N}} k^{2}}{a}$	`\frac{\sum\limits^{^N}_{k=1} k^2}{a}`
product operation	$\prod_{i = 1}^{N} x_{i}$	`\prod_{i=1}^N x_i`
product operation	$\prod_{i = 1}^{N} x_{i}$	`\textstyle \prod_{i=1}^N x_i`
subtractive operation	$∐_{i = 1}^{N} x_{i}$	`\coprod_{i=1}^N x_i`
subtractive operation	$∐_{i = 1}^{N} x_{i}$	`\textstyle \coprod_{i=1}^N x_i`
limit	$lim_{n \to \infty} x_{n}$	`\lim_{n \to \infty}x_n`
limit	$lim_{n \to \infty} x_{n}$	`\textstyle \lim_{n \to \infty}x_n`
limit	$\int_{1}^{3} \frac{e^{3} / x}{x^{2}} d x$	`\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx`
limit	$\int_{1}^{3} \frac{e^{3} / x}{x^{2}} d x$	`\int_{1}^{3}\frac{e^3/x}{x^2}\, dx`
limit	$\int_{- N}^{N} e^{x} d x$	`\textstyle \int\limits_{-N}^{N} e^x dx`
limit	$\int_{- N}^{N} e^{x} d x$	`\textstyle \int_{-N}^{N} e^x dx`
double integral	$\iint_{D} d x d y$	`\iint\limits_D dx\,dy`
triple integral	$\underset{E}{∭} d x d y d z$	`\iiint\limits_E dx\,dy\,dz`
quadruple integral	$\underset{F}{⨌} d x d y d z d t$	`\iiiint\limits_F dx\,dy\,dz\,dt`
path integral	$\int_{(x, y) \in C} x^{3} d x + 4 y^{2} d y$	`\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy`
loop integral	$\oint_{(x, y) \in C} x^{3} d x + 4 y^{2} d y$	`\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy`
intersection	$⋂_{i = 1}^{n} E_{i}$	`\bigcap_{i=1}^n E_i`
union	$⋃_{i = 1}^{n} E_{i}$	`\bigcup_{i=1}^n E_i`

Binomial Coefficient

Type	Sign	LaTeX
binomial coefficient	$(\binom{n}{k})$	`\binom{n}{k}`
small binomial coefficients	$(\binom{n}{k})$	`\tbinom{n}{k}`
big binomial coefficients	$(\binom{n}{k})$	`\dbinom{n}{k}`

Matrix

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

\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{matrix} x & y \\ z & v \end{matrix} ‖

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

[\begin{matrix} 0 & \dots & 0 \\ ⋮ & ⋱ & ⋮ \\ 0 & \dots & 0 \end{matrix}]

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

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

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

(\begin{matrix} x & y \\ z & v \end{matrix})

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

(\begin{matrix} a & b \\ c & d \end{matrix})

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

Array

Sign	LaTeX
![](https://latex.codecogs.com/svg.image?\large&space;\begin{array}{	c	c	c	}a&b&S\hline&space;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}

Equations and Systems of Equations

$\left\{\begin{array}{l}3 x+5 y+z\\7 x-2 y+4 z\\-6 x+3 y+2 z\end{array}\right.$

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

Definition of conditions

| Sign | LaTeX | | —- | —– | $f(n)=\begin{cases}n/2,&\text{if}\,\,n\,\,\text{is even}\\3 n+1,&\text{if}\,\,n\,\,\text{is odd}\end{cases}$

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

Multi-linear Equation

| Sign | LaTeX | | —- | —– | $\begin{aligned}f(x)&=(a+b)^2\\&=a^2+2 a b+b^2\end{aligned}$

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

$\begin{aligned}f(x)&=(a-b)^2\\&=a^2-2 a b+b^2\end{aligned}$

\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2
\end{alignat}

$\begin{array}{ll}z&=a\\f(x,y,z)&=x+y+z\end{array}$

\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}

$\begin{array}{llr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}$

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

Auto-Numbering

\begin{eqnarray}
E = mc^2 \\
e^{i\pi}+1=0
\end{eqnarray}


The entire equation is unnumbered, and you can use the `{equation}`, `{eqnarray}` environments；	$\begin{array}{r} E = m c^{2} \\ e^{i π} + 1 = 0 \end{array}$

\begin{eqnarray*}
E = mc^2 \\
e^{i\pi}+1=0
\end{eqnarray*}


Individual equations are not numbered, you can add the `\nonumber` command after the specified equation；	$\begin{array}{r} (1) & E = m c^{2} \\ e^{i π} + 1 = 0 \end{array}$

\begin{eqnarray}
E = mc^2 \\
e^{i\pi}+1=0 \nonumber
\end{eqnarray}


Individual formulas appear or do not appear numbered, you can use the `\tag{}` or `\notag` command after the formula；	$\begin{array}{r} E = m c^{2} \\ (b) & e^{i π} + 1 = 0 \end{array}$

\begin{eqnarray}
E = mc^2 \notag\\
e^{i\pi}+1=0 \tag{b}
\end{eqnarray}

Bracket Size

Sign	LaTeX
$(((((\dots]]]]]$	`( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]`
${{{{{\dots ⟩ ⟩ ⟩ ⟩ ⟩$	`\{ \bigl \{ \Bigl \{ \biggl \{ \Biggl \{ \dots \Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle`
$\| \| \| \| \| \dots \| \| \| \|$	`\vert \big \vert \Big \vert \bigg \vert \Bigg \vert \dots \Bigg \vert \bigg \vert \Big \vert \big \vert`
$⌊ ⌊ ⌊ ⌊ ⌊ \dots ⌉ ⌉ ⌉ ⌉ ⌉$	`\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil`
$↑ ↑ ↑ ↑ ↑ \dots ⇓ ⇓ ⇓ ⇓ ⇓$	`\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow`
$↕ ↕ ↕ ↕ ↕ \dots ⇕ ⇕ ⇕ ⇕ ⇕$	`\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow`
$/ / / / / \dots \ \ \ \ ∖$	`/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash`

Spaces and Line Breaks

No.	Sign	LaTeX
double space	$a b$	`a \qquad b`
single space	$a b$	`a \quad b`
character space	$a b$	`a\ b`
character spaces in text mode	$a b$	`a \text{ } b`
big space	$a b$	`a\;b`
small space	$a b$	`a\,b`
tiny space	$a b$	`ab`
tiny space（Used to differentiate syntax）	$a b$	`a b`
no space（Used to distinguish multi-letter variables）	$ab$	`\mathit{ab}`

MathJax 3.0 removes the \\ forced line break function in single line equation environment, so the forced line break command \\ can only be used in multi-line environment such as eqnarray, align, array, matrix, etc. Besides, you can use \displaylines{} in line display commands: \displaylines{} forced line break command. In addition, you can use \\displaylines{} to force line breaks in \displaylines{} line display commands:

Sign	LaTeX
$\begin{matrix} y = 1729 x \\ y = 1729 - x \end{matrix}$	`\displaylines{y=1729x \\ y=1729-x}`

Color

When writing LaTeX, it is supported to set Text, Sign or Background to the colors in the table below:

$A p r i c o t$ - `Apricot`	$E m e r a l d$ - `Emerald`	$O l i v e G r e e n$ - `OliveGreen`	$R u b i n e R e d$ - `RubineRed`
$A q u a m a r i n e$ - `Aquamarine`	$F o r e s t G r e e n$ - `ForestGreen`	$O r a n g e$ - `Orange`	$S a l m o n$ - `Salmon`
$B i t t e r s w e e t$ - `Bittersweet`	$F u c h s i a$ - `Fuchsia`	$O r a n g e R e d$ - `OrangeRed`	$S e a G r e e n$ - `SeaGreen`
$B l a c k$ - `Black`	$G o l d e n r o d$ - `Goldenrod`	$O r c h i d$ - `Orchid`	$S e p i a$ - `Sepia`
$B l u e$ - `Blue`	$G r a y$ - `Gray`	$P e a c h$ - `Peach`	$S k y B l u e$ - `SkyBlue`
$B l u e G r e e n$ - `BlueGreen`	$G r e e n$ - `Green`	$P e r i w i n k l e$ - `Periwinkle`	$S p r i n g G r e e n$ - `SpringGreen`
$B l u e v i o l e t$ - `Blueviolet`	$G r e e n Y e l l o w$ - `GreenYellow`	$P i n e G r e e n$ - `PineGreen`	$T a n$ - `Tan`
$B r i c k R e d$ - `BrickRed`	$J u n g l e G r e e n$ - `JungleGreen`	$P l u m$ - `Plum`	$T e a l B l u e$ - `TealBlue`
$B r o w n$ - `Brown`	$L a v e n d e r$ - `Lavender`	$P r o c e s s B l u e$ - `ProcessBlue`	$T h i s t l e$ - `Thistle`
$B u r n t O r a n g e$ - `BurntOrange`	$L i m e G r e e n$ - `LimeGreen`	$P u r p l e$ - `Purple`	$T u r q u o i s e$ - `Turquoise`
$C a d e t B l u e$ - `CadetBlue`	$M a g e n t a$ - `Magenta`	$R a w S i e n n a$ - `RawSienna`	$V i o l e t$ - `Violet`
$C a r n a t i o n P i n k$ - `CarnationPink`	$M a h o g a n y$ - `Mahogany`	$R e d$ - `Red`	$V i o l e t R e d$ - `VioletRed`
$C o r n F l o w e r B l u e$ - `CornFlowerBlue`	$M e l o n$ - `Melon`	$R e d v i o l e t$ - `Redviolet`	$W i l d S t r a w b e r r y$ - `WildStrawberry`
$C e r u l e a n$ - `Cerulean`	$M a r o o n$ - `Maroon`	$R e d O r a n g e$ - `RedOrange`	$w h i t e$ - `white`
$C y a n$ - `Cyan`	$M i d n i g h t B l u e$ - `MidnightBlue`	$R h o d a m i n e$ - `Rhodamine`	$Y e l l o w$ - `Yellow`
$D a n d e l i o n$ - `Dandelion`	$M u l b e r r y$ - `Mulberry`	$R o y a l B l u e$ - `RoyalBlue`	$Y e l l o w G r e e n$ - `YellowGreen`
$D a r k O r c h i d$ - `DarkOrchid`	$N a v y B l u e$ - `NavyBlue`	$R o y a l P u r p l e$ - `RoyalPurple`	$Y e l l o w O r a n g e$ - `YellowOrange`

Font Color

In the formula, you can use {\color{hues}text} to call the color command, where the hues parameter is the font color and the text parameter is the formula content:

Sign	LaTeX
$x^{2} + 2 x - 1$	`{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}`

Background Color

The background color command can be invoked in the text environment using \colorbox{hues}{text}, where the hues parameter is the background color and the text parameter is the equation content:

Sign	LaTeX
$Thistext$	`\colorbox{yellow}{Thistext}`

When this command is used in a math environment, you need to add $\displaystyle + formula$ to the second argument:

Sign	LaTeX
$\frac{a}{b}$	`\colorbox{yellow}{$\displaystyle \frac{a}{b}$}`

Note: Using the $\displaystyle + formula $ syntax in Markdown inline LaTeX formulas $.... $ will cause conflicts when using the $\displaystyle + formula $ syntax in Markdown, so this syntax should only be used for multi-line formulas $$... $$.

RGB Color

The colors of LaTeX formulas can be customized by using the \definecolor command:

Sign	LaTeX
$e^{i π} + 1 = 0$	`\definecolor{mygreen}{RGB}{0,200,0} {\color{mygreen}e^{i \pi} + 1 = 0 }`

Font Style

Font Bold

Sign	LaTeX
$A B C D E F G H I J K L M N O P Q R S T U V W X Y Z$	`\boldsymbol{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$a b c d e f g h i j k l m n o p q r s t u v w x y z$	`\boldsymbol{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\boldsymbol{0123456789}`

Boldface

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathbf{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathbf{0123456789}`

Chalkboard Newspaper

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathbb{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathbb{0123456789}`

Italic

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathit{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathit{0123456789}`

Times New Roman

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathrm{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathrm{0123456789}`

Sans Serif

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathsf{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathsf{0123456789}`

Handwriting

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathcal{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathcal{0123456789}`

Gothic

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}`
$abcdefghijklmnopqrstuvwxyz$	`\mathfrak{abcdefghijklmnopqrstuvwxyz}`
$0123456789$	`\mathfrak{0123456789}`

Small Script

Sign	LaTeX
$ABCDEFGHIJKLMNOPQRSTUVWXYZ$	`{\scriptstyle\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}}`
$abcdefghijklmnopqrstuvwxyz$	`{\scriptstyle\text{abcdefghijklmnopqrstuvwxyz}}`
$0123456789$	`{\scriptstyle\text{0123456789}}`

Sign	LaTeX
$a b c t i n y$	`{\tiny abc tiny}`
$a b c s c r i p t s i z e$	`{\scriptsize abc scriptsize}`
$a b c s m a l l$	`{\small abc small}`
$a b c n o r m a l$	`{\normalsize abc normal}`
$a b c l a r g e$	`{\large abc large}`
$a b c L a r g e$	`{\Large abc Large}`
$a b c L A R G E$	`{\LARGE abc LARGE}`
$a b c h u g e$	`{\huge abc huge}s`
$a b c H u g e$	`{\Huge abc Huge}`