LATEX公式语法
-
see how any formula was written in any question or answer, including this one, right-click on the expression it and choose "Show Math As > TeX Commands". (When you do this, the '$' will not display. Make sure you add these. See the next point.)
-
For inline formulas, enclose the formula in
$...$
. For displayed formulas, use$$...$$
.
These render differently. For example, type
$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$
to show∑ n i=0 i 2 =(n 2 +n)(2n+1)6 ∑i=0ni2=(n2+n)(2n+1)6 (which is inline mode) or type
$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$
to show(which is display mode).∑ i=0 n i 2 =(n 2 +n)(2n+1)6 ∑i=0ni2=(n2+n)(2n+1)6 -
For Greek letters, use
\alpha
,\beta
, …,\omega
:α,β,…ω α,β,…ω. For uppercase, use\Gamma
,\Delta
, …,\Omega
:Γ,Δ,…,Ω Γ,Δ,…,Ω. -
For superscripts and subscripts, use
^
and_
. For example,x_i^2
:x 2 i xi2,\log_2 x
:log 2 x log2x. -
Groups. Superscripts, subscripts, and other operations apply only to the next “group”. A “group” is either a single symbol, or any formula surrounded by curly braces
{
…}
. If you do10^10
, you will get a surprise:10 1 0 1010. But10^{10}
gives what you probably wanted:10 10 1010. Use curly braces to delimit a formula to which a superscript or subscript applies:x^5^6
is an error;{x^y}^z
isx y z xyz, andx^{y^z}
isx y z xyz. Observe the difference betweenx_i^2
x 2 i xi2 andx_{i^2}
x i 2 xi2. -
Parentheses Ordinary symbols
()[]
make parentheses and brackets(2+3)[4+4] (2+3)[4+4]. Use\{
and\}
for curly braces{} {}.These do not scale with the formula in between, so if you write
(\frac{\sqrt x}{y^3})
the parentheses will be too small:(x √ y 3 ) (xy3). Using\left(
…\right)
will make the sizes adjust automatically to the formula they enclose:\left(\frac{\sqrt x}{y^3}\right)
is(x √ y 3 ) (xy3).\left
and\right
apply to all the following sorts of parentheses:(
and)
(x) (x),[
and]
[x] [x],\{
and\}
{x} {x},|
|x| |x|,\langle
and\rangle
⟨x⟩ ⟨x⟩,\lceil
and\rceil
⌈x⌉ ⌈x⌉, and\lfloor
and\rfloor
⌊x⌋ ⌊x⌋. There are also invisible parentheses, denoted by.
:\left.\frac12\right\rbrace
is12 } 12}. -
Sums and integrals
\sum
and\int
; the subscript is the lower limit and the superscript is the upper limit, so for example\sum_1^n
∑ n 1 ∑1n. Don't forget{
…}
if the limits are more than a single symbol. For example,\sum_{i=0}^\infty i^2
is∑ ∞ i=0 i 2 ∑i=0∞i2. Similarly,\prod
∏ ∏,\int
∫ ∫,\bigcup
⋃ ⋃,\bigcap
⋂ ⋂,\iint
∬ ∬. -
Fractions There are two ways to make these.
\frac ab
applies to the next two groups, and producesab ab; for more complicated numerators and denominators use{
…}
:\frac{a+1}{b+1}
isa+1b+1 a+1b+1. If the numerator and denominator are complicated, you may prefer\over
, which splits up the group that it is in:{a+1\over b+1}
isa+1b+1 a+1b+1. -
Fonts
- Use
\mathbb
or\Bbb
for "blackboard bold":CHNQRZ CHNQRZ. - Use
\mathbf
for boldface:ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz. - Use
\mathtt
for "typewriter" font:ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz. - Use
\mathrm
for roman font:ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz. - Use
\mathsf
for sans-serif font:ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz. - Use
\mathcal
for "calligraphic" letters:ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ - Use
\mathscr
for script letters:ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ - Use
\mathfrak
for "Fraktur" (old German style) letters:ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz.
- Use
-
Radical signs Use
sqrt
, which adjusts to the size of its argument:\sqrt{x^3}
x 3 − − √ x3;\sqrt[3]{\frac xy}
xy √ 3 xy3. For complicated expressions, consider using{...}^{1/2}
instead. -
Some special functions such as "lim", "sin", "max", "ln", and so on are normally set in roman font instead of italic font. Use
\lim
,\sin
, etc. to make these:\sin x
sinx sinx, notsin x
sinx sinx. Use subscripts to attach a notation to\lim
:\lim_{x\to 0}
lim x→0 limx→0 -
There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:
\lt \gt \le \ge \neq
<>≤≥≠ <>≤≥≠. You can use\not
to put a slash through almost anything:\not\lt
≮ ≮ but it often looks bad.\times \div \pm \mp
×÷±∓ ×÷±∓.\cdot
is a centered dot:x⋅y x⋅y\cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing
∪∩∖⊂⊆⊊⊃∈∉∅∅ ∪∩∖⊂⊆⊊⊃∈∉∅∅{n+1 \choose 2k}
or\binom{n+1}{2k}
(n+12k) (n+12k)\to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto
→→←⇒⇐↦ →→←⇒⇐↦\land \lor \lnot \forall \exists \top \bot \vdash \vDash
∧∨¬∀∃⊤⊥⊢⊨ ∧∨¬∀∃⊤⊥⊢⊨\star \ast \oplus \circ \bullet
⋆∗⊕∘∙ ⋆∗⊕∘∙\approx \sim \simeq \cong \equiv \prec
≈∼≃≅≡≺ ≈∼≃≅≡≺.\infty \aleph_0
∞ℵ 0 ∞ℵ0\nabla \partial
∇∂ ∇∂\Im \Re
IR ℑℜ- For modular equivalence, use
\pmod
like this:a\equiv b\pmod n
a≡b(modn) a≡b(modn). \ldots
is the dots ina 1 ,a 2 ,…,a n a1,a2,…,an\cdots
is the dots ina 1 +a 2 +⋯+a n a1+a2+⋯+an- Some Greek letters have variant forms:
\epsilon \varepsilon
ϵε ϵε,\phi \varphi
ϕφ ϕφ, and others. Script lowercase l is\ell
ℓ ℓ.
Detexify lets you draw a symbol on a web page and then lists the
TE X TEX symbols that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains a list of currently supportedLA TE X LATEX commands, and one can also check Dr. Carol JVF Burns's page ofTE X TEX Commands Available in MathJax. -
Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in:
a␣b
anda␣␣␣␣b
are bothab ab. To add more space, use\,
for a thin spaceab ab;\;
for a wider spaceab ab.\quad
and\qquad
are large spaces:ab ab,ab ab.To set plain text, use
\text{…}
:{x∈s∣x is extra large} {x∈s∣x is extra large}. You can nest$…$
inside of\text{…}
. -
Accents and diacritical marks Use
\hat
for a single symbolx ^ x^,\widehat
for a larger formulaxy ˆ xy^. If you make it too wide, it will look silly. Similarly, there are\bar
x ¯ x¯ and\overline
xyz ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ xyz¯, and\vec
x ⃗ x→ and\overrightarrow
xy − → xy→ and\overleftrightarrow
xy ← → xy↔. For dots, as inddx xx ˙ =x ˙ 2 +xx ¨ ddxxx˙=x˙2+xx¨, use\dot
and\ddot
. -
Special characters used for MathJax interpreting can be escaped using the
\
character:\$
$ $,\{
{ {,\_
_ _, etc. If you want\
itself, you should use\backslash
∖ ∖, because\\
is for a new line.
(Tutorial ends here.)