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, eta, …, 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(… ight) will make the sizes adjust automatically to the formula they enclose: left(frac{sqrt x}{y^3} ight) is (x  √ y 3  ) (xy3).

   left and ight apply to all the following sorts of parentheses: ( and ) (x) (x), [ and ] [x] [x], { and } {x} {x}, | |x| |x|, langle and  angle ⟨x⟩ ⟨x⟩, lceil and ceil ⌈x⌉ ⌈x⌉, and lfloor and  floor ⌊x⌋ ⌊x⌋. There are also invisible parentheses, denoted by .: left.frac12 ight brace 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 ∫ ∫, igcup ⋃ ⋃, igcap ⋂ ⋂, 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+1over 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 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz.
   • Use mathtt for "typewriter" font: ABCDEFGHIJKLMNOPQRSTUVWXYZ ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz 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.

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 o 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 eq <>≤≥≠ <>≤≥≠. You can use  ot to put a slash through almost anything:  otlt ≮ ≮ but it often looks bad.
    • imes div pm mp ×÷±∓ ×÷±∓. cdot is a centered dot: x⋅y x⋅y
    • cup cap setminus subset subseteq subsetneq supset in otin emptyset varnothing ∪∩∖⊂⊆⊊⊃∈∉∅∅ ∪∩∖⊂⊆⊊⊃∈∉∅∅
    • {n+1 choose 2k} or inom{n+1}{2k} (n+12k) (n+12k)
    • o ightarrow leftarrow Rightarrow Leftarrow mapsto →→←⇒⇐↦ →→←⇒⇐↦
    • land lor lnot forall exists op ot vdash vDash ∧∨¬∀∃⊤⊥⊢⊨ ∧∨¬∀∃⊤⊥⊢⊨
    • star ast oplus circ ullet ⋆∗⊕∘∙ ⋆∗⊕∘∙
    • approx sim simeq cong equiv prec ≈∼≃≅≡≺ ≈∼≃≅≡≺.
    • infty aleph_0 ∞ℵ 0  ∞ℵ0  abla partial ∇∂ ∇∂ Im Re IR ℑℜ
    • For modular equivalence, use pmod like this: aequiv bpmod 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  ext{…}: {x∈s∣x is extra large} {x∈s∣x is extra large}. You can nest $…$ inside of  ext{…}.

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 arear 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 ackslash ∖ ∖, because \ is for a new line.

(Tutorial ends here.)