LATEX公式语法

1.  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.)

2. 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

   ∑ i=0 n i 2 =(n 2 +n)(2n+1)6   ∑i=0ni2=(n2+n)(2n+1)6
   (which is display mode).

3. 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.

4. For superscripts and subscripts, use ^ and _. For example, x_i^2:  x 2 i   xi2, \log_2 x:  log 2 x  log2⁡x.

5. 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 do 10^10, you will get a surprise:  10 1 0  1010. But 10^{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 is  x y  z   xyz, and x^{y^z} is  x y z    xyz. Observe the difference between x_i^2  x 2 i   xi2 and x_{i^2}  x i 2    xi2.

6. 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 is  12 }  12}.

7. 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  ∬  ∬.

8. Fractions There are two ways to make these. \frac ab applies to the next two groups, and produces  ab   ab; for more complicated numerators and denominators use{…}: \frac{a+1}{b+1} is  a+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}is  a+1b+1   a+1b+1.

9. Fonts

   • Use \mathbb or \Bbb for "blackboard bold":  CHNQRZ  CHNQRZ.
   • Use \mathbf for boldface:  ABCDEFGHIJKLMNOPQRSTUVWXYZ  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz  abcdefghijklmnopqrstuvwxyz.
   • Use \mathtt for "typewriter" font:  ABCDEFGHIJKLMNOPQRSTUVWXYZ  ABCDEFGHIJKLMNOPQRSTUVWXYZ  abcdefghijklmnopqrstuvwxyz  abcdefghijklmnopqrstuvwxyz.
   • Use \mathrm for roman font:  ABCDEFGHIJKLMNOPQRSTUVWXYZ  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz  abcdefghijklmnopqrstuvwxyz.
   • Use \mathsf for sans-serif font:  ABCDEFGHIJKLMNOPQRSTUVWXYZ  ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz  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.

10. 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.

11. 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  sin⁡x, not sin x  sinx  sinx. Use subscripts to attach a notation to \lim: \lim_{x\to 0}

    lim x→0   limx→0

12. 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 in  a 1 ,a 2 ,…,a n   a1,a2,…,an \cdots is the dots in  a 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 supported  LA TE X  LATEX commands, and one can also check Dr. Carol JVF Burns's page of  TE X  TEX Commands Available in MathJax.

13. 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 and a␣␣␣␣b are both  ab  ab. To add more space, use \, for a thin space  ab  ab; \; for a wider space  ab  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{…}.

14. Accents and diacritical marks Use \hat for a single symbol  x ^   x^, \widehat for a larger formula  xy 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 in  ddx xx ˙ =x ˙  2 +xx ¨   ddxxx˙=x˙2+xx¨, use \dot and \ddot.

15. 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.)