There are three methods for displaying formulas in Wikipedia: raw HTML, HTML with math templates (abbreviated here as {{math}}), and a subset of LaTeX implemented with the HTML markup <math></math> (referred to as LaTeX in this article). Each method has some advantages and some disadvantages, which have evolved over time with improvements of MediaWiki. The manual of style MOS:MATH has not always evolved accordingly. So the how-to recommendations that appear below may differ from those of the manual of style. In this case, they express a consensus resulting of the practice of most experienced members of WikiProject Mathematics and many discussions at Wikipedia talk:WikiProject Mathematics.
For example, the famous Einstein formula can be entered in raw HTML as {{nowrap|''E'' {{=}} ''mc''<sup>2</sup>}}, which is rendered as E = mc2 (the template {{nowrap}} is here only for avoiding a line break inside the formula). With {{math}}, it can be entered as {{math|''E'' {{=}} ''mc''{{sup|2}}}}, which is rendered as E = mc2. With LaTeX, it is entered as <math>E=mc^2</math>, and rendered as E = m c 2 {\displaystyle E=mc^{2}} .
Variable names and many symbols look very different with raw HTML and the other display methods. This may be confusing in the common case where several methods are used in the same article. Moreover, mathematicians who are used to reading and writing texts written with LaTeX often find the raw HTML rendering awful.
So, raw HTML should normally not be used for new content. However, raw HTML is still present in many mathematical articles. It is generally a good practice to convert it to {{math}} format, but coherency must be respected; that is, such a conversion must be done in a whole article, or at least in a whole section. Moreover, such a conversion must be identified as such in the edit summary, and making other changes in the same edit should be avoided. This is for helping other users to identify changes that are possibly controversial (the "diff" of a conversion may be very large, and may hide other changes).
Converting raw HTML to {{math}} is rather simple: when the formula is enclosed with {{nowrap}}, it suffices to change "nowrap" into "math". However, if the formula contains an equal sign, one has to add 1= just before the formula for avoiding confusion with the template syntax; for example, {{math|1=''E'' = ''mc''{{sup|2}}}}. Also, vertical bars, if any, must either be replaced with {{!}} or avoided by using {{abs}}.
These two ways of writing mathematical formulas each have their advantages and disadvantages. They are both accepted by the manual of style MOS:MATH. The rendering of variable names is very similar. Having a variable name displayed in the same paragraph with {{math}} and <math> is generally not a problem.
The disadvantages of LaTeX are the following: On some browser configurations, LaTeX inline formulas appear with a slight vertical misalignment, or with a font size that may be slightly different from that of the surrounding text. This is not a problem with a block displayed formula, and also typically not with inline formulas that exceed the normal line height marginally (for example formulas with subscripts and superscripts). The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to section headings containing LaTeX formulas do not always work as expected. Finally, having many LaTeX formulas may significantly increase the processing time of a page. LaTeX formulas should be avoided in image captions or footnotes, because when the image is clicked for a larger display or a footnote is selected on a mobile device, LaTeX in the caption or footnote will not render.
Disadvantages of {{math}} include that not all formulas can be displayed, and while it may be possible to display a complicated formula with {{math}}, it may be poorly rendered. Except for the most common symbols such as letters, numerals, and basic punctuation, rendering of Unicode mathematical symbols can be inconsistent in size or alignment where fallback fonts do not match, and some readers may not have any font which includes certain uncommon symbols. Spaces within a formula must be directly managed (for example by including explicit hair or thin spaces). Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read.
The choice between {{math}} and LaTeX depends on the editor. Converting a page from one format to another must be done with stronger reasons than editor preference.
The hidden MathML can be used by screen readers and other assistive technology. To display the MathML in Firefox:
In either case, you must have fonts that support MathML (see developer.mozilla.org) installed on your system. For copy-paste support in Firefox, you can also install MathML Copy.
TeX markup is not the only way to render mathematical formulas. For simple inline formulas, the template {{math}} and its associated templates are often preferred. The following comparison table shows that similar results can be achieved with the two methods. See also Help:Special characters.
TeX syntax TeX rendering HTML syntax HTML rendering<math>\alpha</math> α {\displaystyle \alpha } {{math|''α''}} or {{mvar|α}} α or α <math>f(x) = x^2</math> f ( x ) = x 2 {\displaystyle f(x)=x^{2}} {{math|1=''f''(''x'') = ''x''<sup>2</sup>}} f(x) = x2 <math>\{1,e,\pi\}</math> { 1 , e , π } {\displaystyle \{1,e,\pi \}} {{math|{{mset|1, ''e'', ''π''}}}} {1, e, π} <math>|z| \leq 2</math> | z | ≤ 2 {\displaystyle |z|\leq 2} {{math|{{abs|''z''}} ≤ 2}} |z| ≤ 2
Care should be taken when writing sets within {{math}}, as braces, equal signs, and vertical bars can conflict with template syntax. The {{mset}} template is available for braces, as shown in the example above. Likewise, {{abs}} encloses its parameter inside vertical bars to help with the pipe character conflicting with template syntax. For a single vertical bar, use {{!}}, and for an equal sign, use {{=}}.
Though Unicode characters are generally preferred, sometimes HTML entities are needed to avoid problems with wiki syntax or confusion with other characters:
In the table below, the codes on the left produce the symbols on the right, but these symbols can also be entered directly in the wikitext either by typing them if they are available on the keyboard, by copy-pasting them, or by using menus below the edit windows. (When editing any Wikipedia page in a desktop web browser, use the "Insert" pulldown menu immediately below the article text, or the "Special characters" menu immediately above the article text.) Normally, lowercase Greek letters should be entered in italics, that is, enclosed between two single quotes ('').
α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ ς τ υ φ χ ψ ω
α β γ δ ε ζ
η θ ι κ λ μ ν
ξ ο π ρ σ ς
τ υ φ χ ψ ω
Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω
Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω
∫ ∑ ∏ − ± ∞ ≈ ∝ = ≡ ≠ ≤ ≥ × · ⋅ ÷ ∂ ′ ″ ∇ ‰ ° ∴ ∅
∫ ∑ ∏ − ± ∞
≈ ∝ = ≡ ≠ ≤ ≥
× · ⋅ ÷ ∂ ′ ″
∇ ‰ ° ∴ ∅
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇔ → ↔ ↑ ↓ ℵ - – —
∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀
⇒ ⇔ → ↔ ↑ ↓
ℵ - – —
To avoid line-wrapping in the middle of a formula, use {{math}}. If necessary, a non-breaking space ( ) can be inserted with " ". When an inline formula is long enough, it can be helpful to allow it to break across lines. Whether using LaTeX or templates, split the formula at each acceptable breakpoint into separate <math> tags or {{math}} templates with any binary relations or operators and intermediate whitespace included at the trailing rather than leading end of a part.
Typically whitespace should be a regular space ( ) or none at all. In rare circumstances, such as where one character overlaps another due to one being in italics, a thin space can be added with {{thin space}}.
Math markup goes inside <math>...</math>. Chemistry markup goes inside <math chem>...</math> or <chem>...</chem>. {{tmath|...}} can be used in place of <math>...</math> to avoid line wrapping of adjacent text (with caveats). All these tags use TeX.
The TeX code has to be put literally: MediaWiki templates, predefined templates, and parameters cannot be used within math tags: pairs of double braces are ignored and "#" gives an error message. However, math tags work in the then and else part of #if, etc. See m:Template:Demo of attempt to use parameters within TeX (backlinks edit) for more information.
The now deprecated tag <ce> was considered too ambiguous, and it has been replaced by <chem>.[1]
Some commands need an argument, which has to be given between curly braces {} after the command name. Some commands support optional parameters, which are added after the command name in square brackets []. The general syntax is:
The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts. If you enter them directly in your text, they will normally not render, but rather do things you did not intend.
These characters can be entered by prefixing the escape character backslash \ or using special sequences:
The backslash character \ can not be entered by adding another backslash in front of it (\\); this sequence is used for line breaking. For introducing a backslash in math mode, you can use \backslash instead which gives ∖ {\displaystyle \backslash } .
The command \tilde produces a tilde which is placed over the next letter. For example, \tilde{a} gives a ~ {\displaystyle {\tilde {a}}} . To produce just a tilde character ~, use \tilde{\ } which gives ~ {\displaystyle {\tilde {\ }}} , placing a ~ over an empty box. Alternatively \sim produces ∼ {\displaystyle \sim } , a large centred ~ which may be more appropriate in some situations.
The command \hat produces a hat over the next character, for example \hat{o} produces o ^ {\displaystyle {\hat {o}}} . For a stretchable version, use \widehat{abc} giving a b c ^ {\displaystyle {\widehat {abc}}} . The wedge \wedge is normally used as a mathematical operator ∧ {\displaystyle \wedge } . The sequence {}^\wedge produces ∧ {\displaystyle {}^{\wedge }} the best equivalent to the ASCII caret ^ character.
"Whitespace" characters, such as blank or tab, are treated uniformly as "space" by LaTeX. Several consecutive whitespace characters are treated as one "space". See below for commands that produces spaces of different size.
Environments in LaTeX have a role that is quite similar to commands, but they usually have effect on a wider part of formula. Their syntax is:
The font sizes and types are independent of browser settings or CSS. Font sizes and types will often deviate from what HTML renders. Vertical alignment with the surrounding text can also be a problem; a work-around is described in the "Alignment with normal text flow" section below. The CSS selector of the images is img.tex.
Apart from function and operator names, as is customary in mathematics, variables and letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use \text or \mathrm (formerly \rm). You can also define new function names using \operatorname{...}. For example, \text{abc} gives abc {\displaystyle {\text{abc}}} . \operatorname{...} provides spacing before and after the operator name when appropriate, as when a\operatorname{sn}b is rendered as a sn b {\displaystyle a\operatorname {sn} b} (with space to the left and right of "sn") and a\operatorname{sn}(b+c) as a sn ( b + c ) {\displaystyle a\operatorname {sn} (b+c)} (with space to the left and not to the right). LaTeX's starred version, \operatorname* is not supported, but a workaround is to add \limits instead. For example, \operatorname{sn}_{b>c}(b+c) \qquad \operatorname{sn}\limits_{b>c}(b+c) renders as
LaTeX does not have full support for Unicode characters, and not all characters render. Most Latin characters with accents render correctly. However some do not, in particular those that include multiple diacritics (e.g. with Latin letters used in Vietnamese) or that cannot be precomposed into a single character (such as the uppercase Latin letter W with ring), or that use other diacritics (like the ogonek or the double grave accent, used in Central European languages like Polish, or the horn attached above some vowels in Vietnamese), or other modified letter forms (used in IPA notations, or African languages, or in medieval texts), some digram ligatures (like IJ in Dutch), or Latin letters borrowed from Greek, or small capitals, as well as superscripts and subscript letters. For example, \text{ð} and \text{þ} (used in Icelandic) will give errors.
The normal way of entering quotation marks in text mode (two back ticks for the left and two apostrophes for the right), such as \text{a ``quoted'' word} will not work correctly. As a workaround, you can use the Unicode left and right quotation mark characters, which are available from the "Symbols" dropdown panel beneath the editor: \text{a “quoted” word}.
MediaWiki stores rendered formulas in a cache so that the images of those formulas do not need to be created each time the page is opened by a user. To force the rerendering of all formulas of a page, you must open it with the getter variables action=purge&mathpurge=true. Imagine for example there is a wrong rendered formula in the article Integral. To force the re-rendering of this formula you need to open the URL https://en.wikipedia.org/w/index.php?title=Integral&action=purge&mathpurge=true
Afterwards you need to bypass your browser cache so that the new created images of the formulas are actually downloaded.
Accents and diacritics[edit]\dot{a}, \ddot{a}, \acute{a}, \grave{a} a ˙ , a ¨ , a ´ , a ` {\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}} \check{a}, \breve{a}, \tilde{a}, \bar{a} a ˇ , a ˘ , a ~ , a ¯ {\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}} \hat{a}, \widehat{a}, \vec{a} a ^ , a ^ , a → {\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}} Standard numerical functions[edit] \exp_a b = a^b, \exp b = e^b, 10^m exp a b = a b , exp b = e b , 10 m {\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}} \ln c = \log c, \lg d = \log_{10} d ln c = log c , lg d = log 10 d {\displaystyle \ln c=\log c,\lg d=\log _{10}d} \sin a, \cos b, \tan c, \cot d, \sec f, \csc g sin a , cos b , tan c , cot d , sec f , csc g {\displaystyle \sin a,\cos b,\tan c,\cot d,\sec f,\csc g} \arcsin h, \arccos i, \arctan j arcsin h , arccos i , arctan j {\displaystyle \arcsin h,\arccos i,\arctan j} \sinh k, \cosh l, \tanh m, \coth n sinh k , cosh l , tanh m , coth n {\displaystyle \sinh k,\cosh l,\tanh m,\coth n} \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n sh k , ch l , th m , coth n {\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n} \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q argsh o , argch p , argth q {\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q} \sgn r, \left\vert s \right\vert sgn r , | s | {\displaystyle \operatorname {sgn} r,\left\vert s\right\vert } \min(x,y), \max(x,y) min ( x , y ) , max ( x , y ) {\displaystyle \min(x,y),\max(x,y)} \min x, \max y, \inf s, \sup t min x , max y , inf s , sup t {\displaystyle \min x,\max y,\inf s,\sup t} \lim u, \liminf v, \limsup w lim u , lim inf v , lim sup w {\displaystyle \lim u,\liminf v,\limsup w} \dim p, \deg q, \det m, \ker\phi dim p , deg q , det m , ker ϕ {\displaystyle \dim p,\deg q,\det m,\ker \phi } \injlim, \varinjlim, \projlim, \varprojlim inj lim , lim → , proj lim , lim ← {\displaystyle \injlim ,\varinjlim ,\projlim ,\varprojlim } \Pr j, \hom l, \lVert z \rVert, \arg z Pr j , hom l , ‖ z ‖ , arg z {\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z} Differentials and derivatives[edit] dt, \mathrm{d}t, \partial t, \nabla\psi d t , d t , ∂ t , ∇ ψ {\displaystyle 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} d y / d x , d y / d x , d y d x , d y d x {\displaystyle 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, \left.\frac{\partial^3 f}{\partial^2 x \partial y}\right\vert_{p_0} ∂ 2 ∂ x 1 ∂ x 2 y , ∂ 3 f ∂ 2 x ∂ y | p 0 {\displaystyle {\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y,\left.{\frac {\partial ^{3}f}{\partial ^{2}x\partial y}}\right\vert _{p_{0}}} \prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y ′ , ‵ , f ′ , f ′ , f ″ , f ( 3 ) , y ˙ , y ¨ {\displaystyle \prime ,\backprime ,f^{\prime },f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}} Letter-like symbols or constants[edit] \infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar, \N, \R, \Z, \C, \Q ∞ , ℵ , ∁ , ∍ , ð , Ⅎ , ℏ , N , R , Z , C , Q {\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar ,\mathbb {N} ,\mathbb {R} ,\mathbb {Z} ,\mathbb {C} ,\mathbb {Q} } \Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA ℑ , ı , ȷ , k , ℓ , ℧ , ℘ , ℜ , Ⓢ , § , ¶ , Å {\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\mathrm {\AA} } Modular arithmetic[edit] s_k \equiv 0 \pmod{m} s k ≡ 0 ( mod m ) {\displaystyle s_{k}\equiv 0{\pmod {m}}} a \bmod b a mod b {\displaystyle a{\bmod {b}}} \gcd(m, n), \operatorname{lcm}(m, n) gcd ( m , n ) , lcm ( m , n ) {\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)} \mid, \nmid, \shortmid, \nshortmid ∣ , ∤ , ∣ , ∤ {\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid } \surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}} √ , 2 , 2 n , x 3 + y 3 2 3 {\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{2}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}} +, -, \pm, \mp, \dotplus + , − , ± , ∓ , ∔ {\displaystyle +,-,\pm ,\mp ,\dotplus } \times, \div, \divideontimes, /, \backslash × , ÷ , ⋇ , / , ∖ {\displaystyle \times ,\div ,\divideontimes ,/,\backslash } \cdot, * \ast, \star, \circ, \bullet ⋅ , ∗ ∗ , ⋆ , ∘ , ∙ {\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet } \boxplus, \boxminus, \boxtimes, \boxdot ⊞ , ⊟ , ⊠ , ⊡ {\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot } \oplus, \ominus, \otimes, \oslash, \odot ⊕ , ⊖ , ⊗ , ⊘ , ⊙ {\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot } \circleddash, \circledcirc, \circledast ⊝ , ⊚ , ⊛ {\displaystyle \circleddash ,\circledcirc ,\circledast } \bigoplus, \bigotimes, \bigodot ⨁ , ⨂ , ⨀ {\displaystyle \bigoplus ,\bigotimes ,\bigodot } \{ \}, \O \empty \emptyset, \varnothing { } , ∅ ∅ ∅ , ∅ {\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing } \in, \notin \not\in, \ni, \not\ni ∈ , ∉∉ , ∋ , ∌ {\displaystyle \in ,\notin \not \in ,\ni ,\not \ni } \cap, \Cap, \sqcap, \bigcap ∩ , ⋒ , ⊓ , ⋂ {\displaystyle \cap ,\Cap ,\sqcap ,\bigcap } \cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus ∪ , ⋓ , ⊔ , ⋃ , ⨆ , ⊎ , ⨄ {\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus } \setminus, \smallsetminus, \times ∖ , ∖ , × {\displaystyle \setminus ,\smallsetminus ,\times } \subset, \Subset, \sqsubset ⊂ , ⋐ , ⊏ {\displaystyle \subset ,\Subset ,\sqsubset } \supset, \Supset, \sqsupset ⊃ , ⋑ , ⊐ {\displaystyle \supset ,\Supset ,\sqsupset } \subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq ⊆ , ⊈ , ⊊ , ⊊ , ⊑ {\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq } \supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq ⊇ , ⊉ , ⊋ , ⊋ , ⊒ {\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq } \subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq ⫅ , ⊈ , ⫋ , ⫋ {\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq } \supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq ⫆ , ⊉ , ⫌ , ⫌ {\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq } =, \ne, \neq, \equiv, \not\equiv = , ≠ , ≠ , ≡ , ≢ {\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv } \doteq, \doteqdot, \mathrel{\overset{\underset\mathrm{def}{}}=}, \mathrel{\stackrel\mathrm{def}=}, := ≐ , ≑ , = d e f , = d e f , := {\displaystyle \doteq ,\doteqdot ,\mathrel {\overset {\underset {\mathrm {def} }{}}{=}} ,\mathrel {\stackrel {\mathrm {def} }{=}} ,:=} \sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong ∼ , ≁ , ∽ , ∼ , ≃ , ⋍ , ≂ , ≅ , ≆ {\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong } \approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto ≈ , ≈ , ≊ , ≍ , ∝ , ∝ {\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto } <, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot < , ≮ , ≪ , ≪̸ , ⋘ , ⋘̸ , ⋖ {\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot } >, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot > , ≯ , ≫ , ≫̸ , ⋙ , ⋙̸ , ⋗ {\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot } \le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq ≤ , ≤ , ⪇ , ≦ , ≰ , ≰ , ≨ , ≨ {\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq } \ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq ≥ , ≥ , ⪈ , ≧ , ≱ , ≱ , ≩ , ≩ {\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq } \lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless ≶ , ⋚ , ⪋ , ≷ , ⋛ , ⪌ {\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless } \leqslant, \nleqslant, \eqslantless ⩽ , ⪇ , ⪕ {\displaystyle \leqslant ,\nleqslant ,\eqslantless } \geqslant, \ngeqslant, \eqslantgtr ⩾ , ⪈ , ⪖ {\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr } \lesssim, \lnsim, \lessapprox, \lnapprox ≲ , ⋦ , ⪅ , ⪉ {\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox } \gtrsim, \gnsim, \gtrapprox, \gnapprox ≳ , ⋧ , ⪆ , ⪊ {\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox } \prec, \nprec, \preceq, \npreceq, \precneqq ≺ , ⊀ , ⪯ , ⋠ , ⪵ {\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq } \succ, \nsucc, \succeq, \nsucceq, \succneqq ≻ , ⊁ , ⪰ , ⋡ , ⪶ {\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq } \preccurlyeq, \curlyeqprec ≼ , ⋞ {\displaystyle \preccurlyeq ,\curlyeqprec } \succcurlyeq, \curlyeqsucc ≽ , ⋟ {\displaystyle \succcurlyeq ,\curlyeqsucc } \precsim, \precnsim, \precapprox, \precnapprox ≾ , ⋨ , ⪷ , ⪹ {\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox } \succsim, \succnsim, \succapprox, \succnapprox ≿ , ⋩ , ⪸ , ⪺ {\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox } \parallel, \nparallel, \shortparallel, \nshortparallel ∥ , ∦ , ∥ , ∦ {\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel } \perp, \angle, \sphericalangle, \measuredangle, 45^\circ for degrees ⊥ , ∠ , ∢ , ∡ , 45 ∘ {\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ }} \Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar ◻ , ◻ , ◼ , ⋄ , ◊ , ◊ , ⧫ , ★ {\displaystyle \Box ,\square ,\blacksquare ,\diamond ,\Diamond ,\lozenge ,\blacklozenge ,\bigstar } \bigcirc, \triangle, \bigtriangleup, \bigtriangledown ◯ , △ , △ , ▽ {\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown } \vartriangle, \triangledown △ , ▽ {\displaystyle \vartriangle ,\triangledown } \blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright ▴ , ▾ , ◂ , ▸ {\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright } \forall, \exists, \nexists ∀ , ∃ , ∄ {\displaystyle \forall ,\exists ,\nexists } \therefore, \because, \And ∴ , ∵ , & {\displaystyle \therefore ,\because ,\And } \lor, \vee, \curlyvee, \bigvee
don't use \or which is now deprecated
\land, \wedge, \curlywedge, \bigwedge
don't use \and which is now deprecated
\lnot, \neg, \not\operatorname{R}, \bot, \top ¬ , ¬ , ⧸ R , ⊥ , ⊤ {\displaystyle \lnot ,\neg ,\not \operatorname {R} ,\bot ,\top } \vdash, \dashv, \vDash, \Vdash, \models ⊢ , ⊣ , ⊨ , ⊩ , ⊨ {\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models } \Vvdash, \nvdash, \nVdash, \nvDash, \nVDash ⊪ , ⊬ , ⊮ , ⊭ , ⊯ {\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash } \ulcorner, \urcorner, \llcorner, \lrcorner ⌜ , ⌝ , ⌞ , ⌟ {\displaystyle \ulcorner ,\urcorner ,\llcorner ,\lrcorner } \Rrightarrow, \Lleftarrow ⇛ , ⇚ {\displaystyle \Rrightarrow ,\Lleftarrow } \Rightarrow, \nRightarrow, \Longrightarrow, \implies ⇒ , ⇏ , ⟹ , ⟹ {\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies } \Leftarrow, \nLeftarrow, \Longleftarrow ⇐ , ⇍ , ⟸ {\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow } \Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff ⇔ , ⇎ , ⟺ , ⟺ {\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow ,\iff } \Uparrow, \Downarrow, \Updownarrow ⇑ , ⇓ , ⇕ {\displaystyle \Uparrow ,\Downarrow ,\Updownarrow } \rightarrow, \to, \nrightarrow, \longrightarrow → , → , ↛ , ⟶ {\displaystyle \rightarrow ,\to ,\nrightarrow ,\longrightarrow } \leftarrow, \gets, \nleftarrow, \longleftarrow ← , ← , ↚ , ⟵ {\displaystyle \leftarrow ,\gets ,\nleftarrow ,\longleftarrow } \leftrightarrow, \nleftrightarrow, \longleftrightarrow ↔ , ↮ , ⟷ {\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow } \uparrow, \downarrow, \updownarrow ↑ , ↓ , ↕ {\displaystyle \uparrow ,\downarrow ,\updownarrow } \nearrow, \swarrow, \nwarrow, \searrow ↗ , ↙ , ↖ , ↘ {\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow } \mapsto, \longmapsto ↦ , ⟼ {\displaystyle \mapsto ,\longmapsto } \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons ⇀ , ⇁ , ↼ , ↽ , ↿ , ↾ , ⇃ , ⇂ , ⇌ , ⇋ {\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons } \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright ↶ , ↺ , ↰ , ⇈ , ⇉ , ⇄ , ↣ , ↬ {\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright } \curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft ↷ , ↻ , ↱ , ⇊ , ⇇ , ⇆ , ↢ , ↫ {\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft } \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow ↪ , ↩ , ⊸ , ↭ , ⇝ , ↠ , ↞ {\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow } \amalg \P \S \% \dagger \ddagger \ldots \cdots \vdots \ddots ⨿ ¶ § % † ‡ … ⋯ ⋮ ⋱ {\displaystyle \amalg \P \S \%\dagger \ddagger \ldots \cdots \vdots \ddots } \smile \frown \wr \triangleleft \triangleright ⌣⌢ ≀ ◃ ▹ {\displaystyle \smile \frown \wr \triangleleft \triangleright } \diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp ♢ , ♡ , ♣ , ♠ , ⅁ , ♭ , ♮ , ♯ {\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp } Unsorted (new stuff)[edit] \diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes ╱ , ╲ , ⋅ , ⋉ , ⋊ , ⋋ , ⋌ {\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes } \eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq ≖ , ≗ , ≜ , ≏ , ≎ , ≑ , ≓ , ≒ {\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq } \intercal \barwedge \veebar \doublebarwedge \between \pitchfork ⊺ , ⊼ , ⊻ , ⩞ , ≬ , ⋔ {\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork } \vartriangleleft \ntriangleleft \vartriangleright \ntriangleright ⊲ , ⋪ , ⊳ , ⋫ {\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright } \trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq ⊴ , ⋬ , ⊵ , ⋭ {\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq } Feature Syntax How it looks rendered Superscript a^2, a^{x+3} a 2 , a x + 3 {\displaystyle a^{2},a^{x+3}} Subscript a_2 a 2 {\displaystyle a_{2}} Grouping 10^{30} a^{2+2} 10 30 a 2 + 2 {\displaystyle 10^{30}a^{2+2}} a_{i,j} b_{f'} a i , j b f ′ {\displaystyle a_{i,j}b_{f'}} Combining sub & super without and with horizontal separation x_2^3 x 2 3 {\displaystyle x_{2}^{3}} {x_2}^3 x 2 3 {\displaystyle {x_{2}}^{3}} Super super 10^{10^{8}} 10 10 8 {\displaystyle 10^{10^{8}}} Preceding and/or additional sub & super \sideset{_1^2}{_3^4}\prod_a^b ∏ 1 2 ∏ 3 4 a b {\displaystyle \sideset {_{1}^{2}}{_{3}^{4}}\prod _{a}^{b}} {}_1^2\!\Omega_3^4 1 2 Ω 3 4 {\displaystyle {}_{1}^{2}\!\Omega _{3}^{4}} Stacking \overset{\alpha}{\omega} ω α {\displaystyle {\overset {\alpha }{\omega }}} \underset{\alpha}{\omega} ω α {\displaystyle {\underset {\alpha }{\omega }}} \overset{\alpha}{\underset{\gamma}{\omega}} ω γ α {\displaystyle {\overset {\alpha }{\underset {\gamma }{\omega }}}} \stackrel{\alpha}{\omega} ω α {\displaystyle {\stackrel {\alpha }{\omega }}} Derivatives x', y'', f', f'' x ′ , y ″ , f ′ , f ″ {\displaystyle x',y'',f',f''} x^\prime, y^{\prime\prime} x ′ , y ′ ′ {\displaystyle x^{\prime },y^{\prime \prime }} Derivative dots \dot{x}, \ddot{x} x ˙ , x ¨ {\displaystyle {\dot {x}},{\ddot {x}}} Underlines, overlines, vectors \hat a \ \bar b \ \vec c a ^ b ¯ c → {\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}} \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} a b → c d ← d e f ^ {\displaystyle {\overrightarrow {ab}}\ {\overleftarrow {cd}}\ {\widehat {def}}} \overline{g h i} \ \underline{j k l} g h i ¯ j k l _ {\displaystyle {\overline {ghi}}\ {\underline {jkl}}} Arc (workaround) \overset{\frown} {AB} A B ⌢ {\displaystyle {\overset {\frown }{AB}}} Arrows A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C A ← n + μ − 1 B → T n ± i − 1 C {\displaystyle A{\xleftarrow {n+\mu -1}}B{\xrightarrow[{T}]{n\pm i-1}}C} Overbraces \overbrace{ 1+2+\cdots+100 }^{5050} 1 + 2 + ⋯ + 100 ⏞ 5050 {\displaystyle \overbrace {1+2+\cdots +100} ^{5050}} Underbraces \underbrace{ a+b+\cdots+z }_{26} a + b + ⋯ + z ⏟ 26 {\displaystyle \underbrace {a+b+\cdots +z} _{26}} Sum \sum_{k=1}^N k^2 ∑ k = 1 N k 2 {\displaystyle \sum _{k=1}^{N}k^{2}} Sum (force \textstyle) \textstyle \sum_{k=1}^N k^2 ∑ k = 1 N k 2 {\displaystyle \textstyle \sum _{k=1}^{N}k^{2}} Sum in a fraction (default \textstyle) \frac{\sum_{k=1}^N k^2}{a} ∑ k = 1 N k 2 a {\displaystyle {\frac {\sum _{k=1}^{N}k^{2}}{a}}} Sum in a fraction (force \displaystyle) \frac{\displaystyle \sum_{k=1}^N k^2}{a} ∑ k = 1 N k 2 a {\displaystyle {\frac {\displaystyle \sum _{k=1}^{N}k^{2}}{a}}} Sum in a fraction (alternative limits style) \frac{\sum\limits^{N}_{k=1} k^2}{a} ∑ k = 1 N k 2 a {\displaystyle {\frac {\sum \limits _{k=1}^{N}k^{2}}{a}}} Product \prod_{i=1}^N x_i ∏ i = 1 N x i {\displaystyle \prod _{i=1}^{N}x_{i}} Product (force \textstyle) \textstyle \prod_{i=1}^N x_i ∏ i = 1 N x i {\displaystyle \textstyle \prod _{i=1}^{N}x_{i}} Coproduct \coprod_{i=1}^N x_i ∐ i = 1 N x i {\displaystyle \coprod _{i=1}^{N}x_{i}} Coproduct (force \textstyle) \textstyle \coprod_{i=1}^N x_i ∐ i = 1 N x i {\displaystyle \textstyle \coprod _{i=1}^{N}x_{i}} Limit \lim_{n \to \infty}x_n lim n → ∞ x n {\displaystyle \lim _{n\to \infty }x_{n}} Limit (force \textstyle) \textstyle \lim_{n \to \infty}x_n lim n → ∞ x n {\displaystyle \textstyle \lim _{n\to \infty }x_{n}} Integral \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx ∫ 1 3 e 3 / x x 2 d x {\displaystyle \int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx} Integral (alternative limits style) \int_{1}^{3}\frac{e^3/x}{x^2}\, dx ∫ 1 3 e 3 / x x 2 d x {\displaystyle \int _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx} Integral (force \textstyle) \textstyle \int\limits_{-N}^{N} e^x dx ∫ − N N e x d x {\displaystyle \textstyle \int \limits _{-N}^{N}e^{x}dx} Integral (force \textstyle, alternative limits style) \textstyle \int_{-N}^{N} e^x dx ∫ − N N e x d x {\displaystyle \textstyle \int _{-N}^{N}e^{x}dx} Double integral \iint\limits_D dx\,dy ∬ D d x d y {\displaystyle \iint \limits _{D}dx\,dy} Triple integral \iiint\limits_E dx\,dy\,dz ∭ E d x d y d z {\displaystyle \iiint \limits _{E}dx\,dy\,dz} Quadruple integral \iiiint\limits_F dx\,dy\,dz\,dt ⨌ F d x d y d z d t {\displaystyle \iiiint \limits _{F}dx\,dy\,dz\,dt} Line or path integral \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy ∫ ( x , y ) ∈ C x 3 d x + 4 y 2 d y {\displaystyle \int _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy} Closed line or path integral \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy ∮ ( x , y ) ∈ C x 3 d x + 4 y 2 d y {\displaystyle \oint _{(x,y)\in C}x^{3}\,dx+4y^{2}\,dy} Intersections \bigcap_{i=1}^n E_i ⋂ i = 1 n E i {\displaystyle \bigcap _{i=1}^{n}E_{i}} Unions \bigcup_{i=1}^n E_i ⋃ i = 1 n E i {\displaystyle \bigcup _{i=1}^{n}E_{i}} Feature Syntax How it looks rendered Fractions \frac{2}{4}=0.5 or {2 \over 4}=0.5 2 4 = 0.5 {\displaystyle {\frac {2}{4}}=0.5} Small fractions (force \textstyle) \tfrac{2}{4} = 0.5 2 4 = 0.5 {\displaystyle {\tfrac {2}{4}}=0.5} Large (normal) fractions (force \displaystyle) \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a 2 4 = 0.5 2 c + 2 d + 2 4 = a {\displaystyle {\dfrac {2}{4}}=0.5\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {2}{4}}}}}}=a} Large (nested) fractions \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a 2 c + 2 d + 2 4 = a {\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a} Cancellations in fractions \cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2} x 1 + y y = x 2 {\displaystyle {\cfrac {x}{1+{\cfrac {\cancel {y}}{\cancel {y}}}}}={\cfrac {x}{2}}} Binomial coefficients \binom{n}{k} ( n k ) {\displaystyle {\binom {n}{k}}} Small binomial coefficients (force \textstyle) \tbinom{n}{k} ( n k ) {\displaystyle {\tbinom {n}{k}}} Large (normal) binomial coefficients (force \displaystyle) \dbinom{n}{k} ( n k ) {\displaystyle {\dbinom {n}{k}}} Matrices
\begin{matrix}
-x & y \\
z & -v
\end{matrix}
− x y z − v {\displaystyle {\begin{matrix}-x&y\\z&-v\end{matrix}}}
\begin{vmatrix}
-x & y \\
z & -v
\end{vmatrix}
| − x y z − v | {\displaystyle {\begin{vmatrix}-x&y\\z&-v\end{vmatrix}}}
\begin{Vmatrix}
-x & y \\
z & -v
\end{Vmatrix}
‖ − x y z − v ‖ {\displaystyle {\begin{Vmatrix}-x&y\\z&-v\end{Vmatrix}}}
\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}
[ 0 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ 0 ] {\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}}
\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}
{ x y z v } {\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}}
\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}
( x y z v ) {\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
( a b c d ) {\displaystyle {\bigl (}{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}{\bigr )}} Case distinctions
f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}
f ( n ) = { n / 2 , if n is even 3 n + 1 , if n is odd {\displaystyle f(n)={\begin{cases}n/2,&{\text{if }}n{\text{ is even}}\\3n+1,&{\text{if }}n{\text{ is odd}}\end{cases}}} Simultaneous equations
\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
{ 3 x + 5 y + z 7 x − 2 y + 4 z − 6 x + 3 y + 2 z {\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}} Multiline equations
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
f ( x ) = ( a + b ) 2 = a 2 + 2 a b + b 2 {\displaystyle {\begin{aligned}f(x)&=(a+b)^{2}\\&=a^{2}+2ab+b^{2}\\\end{aligned}}}
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
f ( x ) = ( a − b ) 2 = a 2 − 2 a b + b 2 {\displaystyle {\begin{alignedat}{2}f(x)&=(a-b)^{2}\\&=a^{2}-2ab+b^{2}\\\end{alignedat}}} Multiline equations with multiple alignments per row
\begin{align}
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\
\end{align}
f ( a , b ) = ( a + b ) 2 = ( a + b ) ( a + b ) = a 2 + a b + b a + b 2 = a 2 + 2 a b + b 2 {\displaystyle {\begin{aligned}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{aligned}}}
\begin{alignat}{3}
f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\
& = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\
\end{alignat}
f ( a , b ) = ( a + b ) 2 = ( a + b ) ( a + b ) = a 2 + a b + b a + b 2 = a 2 + 2 a b + b 2 {\displaystyle {\begin{alignedat}{3}f(a,b)&=(a+b)^{2}&&=(a+b)(a+b)\\&=a^{2}+ab+ba+b^{2}&&=a^{2}+2ab+b^{2}\\\end{alignedat}}} Multiline equations (must define number of columns used ({lcl})) (should not be used unless needed)
\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
z = a f ( x , y , z ) = x + y + z {\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}} Multiline equations (more)
\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
z = a f ( x , y , z ) = x + y + z {\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}} Multiline alignment using & to left align (top example) versus && to right align (bottom example) the last column
\begin{alignat}{4}
F:\; && C(X) && \;\to\; & C(X) \\
&& g && \;\mapsto\; & g^2
\end{alignat}
\begin{alignat}{4}
F:\; && C(X) && \;\to\; && C(X) \\
&& g && \;\mapsto\; && g^2
\end{alignat}
F : C ( X ) → C ( X ) g ↦ g 2 {\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&C(X)\\&&g&&\;\mapsto \;&g^{2}\end{alignedat}}}
F : C ( X ) → C ( X ) g ↦ g 2 {\displaystyle {\begin{alignedat}{4}F:\;&&C(X)&&\;\to \;&&C(X)\\&&g&&\;\mapsto \;&&g^{2}\end{alignedat}}}
Breaking up a long expression so that it wraps when necessary (this sometimes requires workarounds for correct spacing)The function <math>f</math> is defined by
<math>f(x) = {}</math><math display=inline>\sum_{n=0}^\infty a_n x^n = {}</math><math>a_0+a_1x+a_2x^2+\cdots.</math>
The function f {\displaystyle f} is defined by f ( x ) = {\displaystyle f(x)={}} ∑ n = 0 ∞ a n x n = {\textstyle \sum _{n=0}^{\infty }a_{n}x^{n}={}} a 0 + a 1 x + a 2 x 2 + ⋯ . {\displaystyle a_{0}+a_{1}x+a_{2}x^{2}+\cdots .} Arrays
\begin{array}{|c|c|c|} a & b & S \\
\hline
0 & 0 & 1 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\end{array}
a b S 0 0 1 0 1 1 1 0 1 1 1 0 {\displaystyle {\begin{array}{|c|c|c|}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}
The <math> tag can take a display attribute with possible values of inline and block.
If the value of the display attribute is inline, the contents will be rendered in inline mode: there will be no new paragraph for the equation and the operators will be rendered to consume only a small amount of vertical space.
The next line-width is not disturbed by large operators.
The quotation marks around inline are optional and display=inline is also valid.[2]
Technically, the command \textstyle will be added to the user input before the TeX command is passed to the renderer. The result will be displayed without further formatting by outputting the image or MathML element to the page.
In block-style the equation is rendered in its own paragraph and the operators are rendered consuming less horizontal space. The equation is indented.
The sum ∑ i = 0 ∞ 2 − i {\displaystyle \sum _{i=0}^{\infty }2^{-i}} converges to 2.
Technically, the command \displaystyle will be added to the user input (if the user input does not already contain the string \displaystyle or \align) before the TeX command is passed to the renderer. The result will be displayed in a new paragraph. Therefore, the style of the MathImage is altered, i.e. the style attribute "display:block;margin:auto" is added. For MathML it is ensured that display=inline is replaced by display block which produces a new paragraph
If nothing is specified, the equation is rendered in the same display style as "block", but without using a new paragraph. If the equation does appear on a line by itself, it is not automatically indented.
The sum ∑ i = 0 ∞ 2 − i {\displaystyle \sum _{i=0}^{\infty }2^{-i}} converges to 2.
The next line-width is disturbed by large operators.
converges to 2.
The templates {{NumBlk}} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax:
Later on, the text can refer to this equation by its number using syntax like this:
The equation number produced by {{EquationNote}} is a link that the user can click to go immediately to the cited equation.
Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.
Equations can use color with the \color command. For example,
The \color command colors all symbols to its right. However, if the \color command is enclosed in a pair of braces (e.g. {\color{Red}...}) then no symbols outside of those braces are affected.
Some color names are predeclared according to the following table, you can use them directly for the rendering of formulas (or for declaring the intended color of the page background).
Color should not be used as the only way to identify something, because it will become meaningless on black-and-white media or for color-blind people. See WP:Manual of Style (accessibility)#Color.
Latex does not have a command for setting the background color. The most effective way of setting a background color is by setting a CSS styling rule for a table cell:
TeX handles most spacing automatically, but you may sometimes want manual control.
Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX):
This can be remedied by putting a pair of braces { } around the whole expression:
When relational symbols such as ↑ {\displaystyle \uparrow } are employed as ordinary symbols, for example in bra–ket notation, additional spacing may have to be avoided:
The phantom commands create empty horizontal and/or vertical space the same height and/or width of the argument.
an inline expression like ∫ − N N e x d x {\displaystyle \int _{-N}^{N}e^{x}\,dx} should look good.
If you need to align it otherwise, use <math style="vertical-align:-100%;">...</math> and play with the vertical-align argument until you get it right; however, how it looks may depend on the browser and the browser settings.
If you rely on this workaround, if and when the rendering on the server gets fixed in a future release, this extra manual offset will suddenly make every affected formula align incorrectly. So use it sparingly, if at all.
The following integral operators that are not supported by the default font of MathJax 2.7 are available
they have poor horizontal spacing, generate cropped SVG images unless used with other tall characters, and appear different from the usual integral symbol \int:
Elements which are not yet implemented are \oiint, namely a two-fold integral \iint ( ∬ {\displaystyle \iint } ) with a circular curve through the centre of the two integrals, and similarly \oiiint, a circular curve through three integrals. In contrast, \oint ( ∮ {\displaystyle \oint } ) exists for the single dimension (integration over a curved line within a plane or any space with higher dimension).
These elements appear in many contexts: \oiint denotes a surface integral over the closed 2d boundary of a 3d region (which occurs in much of 3d vector calculus and physical applications – like Maxwell's equations), likewise \oiiint denotes integration over the closed 3d boundary (surface volume) of a 4d region, and they would be strong candidates for the next TeX version. As such there are a lot of workarounds in the present version.
However, since no standardisation exists as yet, any workaround like this (which uses many \! symbols for backspacing) should be avoided, if possible. See below for a possibility using PNG image enforcement.
Note that \iint (the double integral) and \iiint (the triple integral) are still not kerned as they should preferably be, and are currently rendered as if they were successive \int symbols; this is not a major problem for reading the formulas, even if the integral symbols before the last one do not have bounds, so it's best to avoid backspacing "hacks" as they may be inconsistent with a possible future better implementation of integrals symbols (with more precisely computed kerning positions).
These symbols are available as PNG images which are also integrated into two templates, {{oiint}} and {{oiiint}}, which take care of the formatting around the symbols.
P = {\displaystyle \mathbf {P} =} ∂ Ω {\displaystyle \scriptstyle \partial \Omega } T ⋅ d 3 Σ {\displaystyle \mathbf {T} \cdot {\mathrm {d} }^{3}{\boldsymbol {\Sigma }}}
= 0 {\displaystyle =0}
Some variants of \oiint and \oiiint have arrows on them to indicate the sense of integration, such as a line integral around a closed curve in the clockwise sense, and higher dimensional analogues. These are not implemented in TeX on Wikipedia either, although the template {{intorient}} is available - see link for details.
\overarc is not yet implemented to display the arc notation. However, there exists a workaround: use \overset{\frown}{AB}, which gives
\dddot is not implemented. For a workaround use \overset{...}{x}, which gives
x . . . {\displaystyle {\overset {...}{x}}} .
The starred version of \operatorname is not currently supported. A workaround for
Strikethrough like \sout or \st is not implemented, nor is overlapping like \rlap. This means struck characters like ƛ are difficult to type, except the hardcoded \hbar. A workaround suffix for a normal strikethrough is q \!\!\!\frac{}{\ }, and for elevated strikethrough is \lambda \!\!\!^{{}^\underline{\ \ }}, which give
Formatting in \text is not supported. In other words, you can't use:
More specifically, in Mathoid's MathJax, no processing is done to the contents of \text at all. The texvcjs component blocks the use of macros, but another way this behavior leaks through is in the processing of quotation marks, where the Unicode version must be used instead of `:
The current image-based implementation precludes automatic line-breaking of inline formulae after binary operators and "=" as seen in TeX. The only workarounds are to not write long formulae inline, or to split the formula into separate parts at each acceptable break point.
Non-ASCII Unicode characters like π work in MathML, but not in Mathoid (server-side MathJax in SVG/PNG mode, after validation by texvcjs). They should be avoided for maximum compatibility.
MathJax itself supports Unicode characters in \text{}, but the texvcjs validator insists on blocking them (replicating old texvc behavior). A formal feature request and discussion is required to fix this.
A rare but very frustrating cause of inexplicable syntax errors is invisible Unicode characters copied from some other source. For example, the Windows Calculator includes Unicode Bidirectional text control characters in its output: U+202D (left-to-right override) at the beginning and U+202C (pop directional formatting) at the end. These characters can be invisibly pasted into the Wikipedia editor, but will cause Failed to parse (syntax error): messages from the LaTeX renderer, despite the source appearing to be correct. It can usually be fixed by deleting and manually retyping the beginning and end of the pasted text.
The texvc processor accepted some non-standard control sequences. These are now deprecated for Wikipedia use because the MathJax-based renderers do not support them. This is part of an effort to update the math engine. See mw:Extension:Math/Roadmap for details. A bot User:Texvc2LaTeXBot will replace this syntax on the English Wikipedia.
texvc syntax Suggested replacement Comment $ \$ redefinition would involve changing the character code % \% redefinition would involve changing the character code \or \lor causes the teubner TeX package to fail[4] \and \land causes normal align environment to fail \pagecolor (remove) not needed and not working anymore, done manually \part \partial acceptable if the document doesn't use sectioning with\part. \ang \angle this only conflicts with siunitx package. \C \Complex conflicts with puenc.def e.g. from hyperref package \H \mathbb{H} conflicts with text command \H{o}, which is ő. \bold \mathbf \Bbb \mathbb
There are three ways to render chemical sum formulas as used in chemical equations:
<chem>X</chem> is short for <math chem>\ce{X}</math> (where X is a chemical sum formula)
Technically, <math chem> is a math tag with the extension mhchem enabled, according to the MathJax documentation.
If the formula reaches a certain "complexity", spaces might be ignored (<chem>A + B</chem> might be rendered as if it were <chem>A+B</chem> with a positive charge). In that case, write <chem>A{} + B</chem> (and not <chem>{A} + {B}</chem> as was previously suggested). This will allow auto-cleaning of formulas once the bug is fixed and/or a newer version of mhchem is available.
Please note that there are still major issues with mhchem support in MediaWiki. Some issues can be solved by enabling the extension using <math chem> and formatting individual items with \ce. For example,
{{chem}} {{chem2}} Equivalent HTML Markup Renders as
<chem>H2O</chem>
H 2 O {\displaystyle {\ce {H2O}}}
<chem>Sb2O3</chem>
Sb 2 O 3 {\displaystyle {\ce {Sb2O3}}}
<chem>(NH4)2S</chem>
( NH 4 ) 2 S {\displaystyle {\ce {(NH4)2S}}}
Markup Renders as{{chem|H|2|O}}
H
2O
{{chem|Sb|2|O|3}}
Sb
2O
3
{{chem|({{chem|N|H|4}})|2|S}}
(NH
4)
2S
{{chem2|H2O}}
H2O
{{chem2|Sb2O3}}
Sb2O3
{{chem2|(NH4)2S}}
(NH4)2S
Markup Renders asH<sub>2</sub>O
H2O
Sb<sub>2</sub>O<sub>3</sub>
Sb2O3
(NH<sub>4</sub>)<sub>2</sub>S
(NH4)2S
mhchem Equivalent{{chem}} and HTML {{chem2}} Markup Renders as
<chem>C6H5-CHO</chem>
C 6 H 5 − CHO {\displaystyle {\ce {C6H5-CHO}}}
<chem>A-B=C#D</chem>
A − B = C ≡ D {\displaystyle {\ce {A-B=C#D}}}
Markup Renders as{{chem|C|6|H|5}}-CHO
<br/>
C<sub>6</sub>H<sub>5</sub>-CHO
C
6H
5-CHO
C6H5-CHO
A-B=C≡D
N/A
Markup Renders as{{chem2|C6H5\sCHO}}
C6H5−CHO
{{chem2|1=A\sB=C≡D}}
A−B=C≡D
mhchem{{chem}} {{chem2}} Equivalent HTML Markup Renders as
<chem>H+</chem>
H + {\displaystyle {\ce {H+}}}
<chem>NO3-</chem>
NO 3 − {\displaystyle {\ce {NO3-}}}
<chem>CrO4^2-</chem>
CrO 4 2 − {\displaystyle {\ce {CrO4^2-}}}
<chem>AgCl2-</chem>
AgCl 2 − {\displaystyle {\ce {AgCl2-}}}
<chem>[AgCl2]-</chem>
[ AgCl 2 ] − {\displaystyle {\ce {[AgCl2]-}}}
<chem>Y^99+</chem>
<chem>Y^{99+}</chem>
Y 99 + {\displaystyle {\ce {Y^99+}}}
Y 99 + {\displaystyle {\ce {Y^{99+}}}}
{{chem|H|+}}
H+
{{chem|N|O|3|-}}
NO−
3
{{chem|Cr|O|4|2-}}
CrO2−
4
{{chem|Ag|Cl|2|-}}
AgCl−
2
{{chem|[{{chem|Ag|Cl|2}}]|-}}
[AgCl
2]−
{{chem|Y|99+}}
Y99+
{{chem2|H+}}
H+
{{chem2|NO3(-)}}
NO−3
{{chem2|CrO4(2-)}}
CrO2−4
{{chem2|AgCl2(-)}}
AgCl−2
{{chem2|[AgCl2](-)}}
[AgCl2]−
{{chem2|Y(99+)}}
Y99+
Markup Renders asH<sup>+</sup>
H+
NO<sub>3</sub><sup>−</sup>
NO3−
CrO<sub>4</sub><sup>2-</sup>
CrO42-
AgCl<sub>2</sub><sup>−</sup>
AgCl2−
[AgCl<sub>2</sub>]<sup>−</sup>
[AgCl2]−
Y<sup>99+</sup>
Y99+
mhchem{{chem}} {{chem2}} Markup Renders as
<chem>MgSO4.7H2O</chem>
MgSO 4 ⋅ 7 H 2 O {\displaystyle {\ce {MgSO4.7H2O}}}
<chem>KCr(SO4)2*12H2O</chem>
KCr ( SO 4 ) 2 ⋅ 12 H 2 O {\displaystyle {\ce {KCr(SO4)2*12H2O}}}
<chem>CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O</chem>
CaSO 4 ⋅ 1 2 H 2 O + 1 1 2 H 2 O ⟶ CaSO 4 ⋅ 2 H 2 O {\displaystyle {\ce {CaSO4.1/2H2O + 1\!1/2 H2O -> CaSO4.2H2O}}}
<chem>25/2 O2 + C8H18 -> 8 CO2 + 9 H2O</chem>
25 2 O 2 + C 8 H 18 ⟶ 8 CO 2 + 9 H 2 O {\displaystyle {\ce {25/2 O2 + C8H18 -> 8 CO2 + 9 H2O}}}
Markup Renders as{{chem|Mg|S|O|4}}·7{{chem|H|2|O}}MgSO
4·7H
2O
{{chem|K|Cr|({{chem|S|O|4}})|2}}·12{{chem|H|2|O}}KCr(SO
4)
2·12H
2O
{{chem|Ca|S|O|4}}·½{{chem|H|2|O}} + 1½{{chem|H|2|O}} → {{chem|Ca|S|O|4}}·2{{chem|H|2|O}}CaSO
4·½H
2O + 1½H
2O → CaSO
4·2H
2O
{{frac|25|2}}{{chem|O|2}} + {{chem|C|8|H|18}} → 8{{chem|C|O|2}} + 9{{chem|H|2|O}}25⁄2O
2 + C
8H
18 → 8CO
2 + 9H
2O
{{chem2|MgSO4*7H2O}}
MgSO4·7H2O
{{chem2|KCr(SO4)2*12H2O}}
KCr(SO4)2·12H2O
{{chem2|2CaSO4*H2O + 3H2O -> 2CaSO4*2H2O}}
2CaSO4·H2O + 3H2O → 2CaSO4·2H2O
{{chem2|25 O2 + 2 C8H18 -> 16 CO2 + 18 H2O}}
25 O2 + 2 C8H18 → 16 CO2 + 18 H2O
{{chem}} Markup
25 {{chem|link=oxygen|O|2}} + 2 {{chem|link=octane|C|8|H|18}} → 16 {{chem|link=Carbon dioxide|C|O|2}} + 18 {{chem|link=water|H|2|O}} Renders as
25
O+ 2
C→ 16
CO+ 18
H{{chem2}} Markup
{{chem2|25 [[oxygen|O2]] + 2 [[octane|C8H18]] -> 16 [[Carbon dioxide|CO2]] + 18 [[water|H2O]]}} Renders as 25 O2 + 2 C8H18 → 16 CO2 + 18 H2O mhchem Markup
<chem>{C_\mathit{x}H_\mathit{y}} + \mathit{z}O2 -> {\mathit{x}CO2} + \frac{\mathit{y}}{2}H2O</chem>{{chem}} Markup
{{chem|C|''x''|H|''y''}} + ''z''{{chem|O|2}} → ''x''{{chem|C|O|2}} + {{frac|''y''|2}}{{chem|H|2|O}} Renders as
C
xH
y + zO
2 → xCO
2 + y/2H
2O
{{chem2}} Markup
{{chem2|C_{''x''}H_{''y''} + ''z'' O2 -> ''x'' CO2}} + {{sfrac|''y''|2}} {{chem2| H2O}} Renders as
CxHy + z O2 → x CO2 + y/2 H2O
mhchem Markup<chem>Fe^{II}Fe^{III}2O4</chem> Renders as Fe II Fe 2 III O 4 {\displaystyle {\ce {Fe^{II}Fe^{III}2O4}}} {{chem}} with <sup>...</sup> Markup
{{chem|Fe|<sup>II</sup>|Fe|<sup>III</sup>|2|O|4}} Renders as
FeIIFeIII
2O
4
{{chem2}} Markup
{{chem2|Fe^{II}Fe^{III}2O4}} Renders as
FeIIFeIII2O4
mhchem Equivalent{{chem}} and HTML {{chem2}} Markup Renders as
<chem>\mu-Cl</chem>μ − Cl {\displaystyle {\ce {\mu-Cl}}}
<chem>[Fe(\eta^5-C5H5)2]</chem>[ Fe ( η 5 − C 5 H 5 ) 2 ] {\displaystyle {\ce {[Fe(\eta^5-C5H5)2]}}}
Markup Renders as''μ''-Clμ-Cl
[{{chem|Fe|(''η''<sup>5</sup>-{{chem|C|5|H|5}})|2}}]
<br/>
[Fe(''η''<sup>5</sup>-C<sub>5</sub>H<sub>5</sub>)<sub>2</sub>]
[Fe(η5-C
5H
5)
2]
[Fe(η5-C5H5)2]
{{chem2|''μ''\sCl}}
μ−Cl
{{chem2|[Fe(''\h''^{5}\sC5H5)2]}}
[Fe(η5−C5H5)2]
mhchem Equivalent{{chem}} and HTML Markup Renders as
<chem>^{227}_{90}Th+</chem>Th + 90 227 {\displaystyle {\ce {^{227}_{90}Th+}}}
<chem>^0_{-1}n-</chem>n − − 1 0 {\displaystyle {\ce {^0_{-1}n-}}}
Markup Renders as{{chem|227|90|Th|+}}
227
90Th+
{{chem|0|-1}}n<sup>−</sup>
0
-1n−
Subscripting states is not an IUPAC recommendation.
mhchem{{chem}} Markup Renders as
<chem>H2_{(aq)}</chem>
H 2 ( aq ) {\displaystyle {\ce {H2_{(aq)}}}}
<chem>CO3^{2-}(aq)</chem>
CO 3 2 − ( aq ) {\displaystyle {\ce {CO3^{2-}(aq)}}}
Markup Renders as{{chem|H|2(aq)}}
H
2(aq)
{{chem|C|O|3|2-}}(aq)
CO2−
3(aq)
<chem>Ba^2+ + SO4^{2-} -> BaSO4(v)</chem> Renders as Ba 2 + + SO 4 2 − ⟶ BaSO 4 ↓ {\displaystyle {\ce {Ba^2+ + SO4^{2-}-> BaSO4(v)}}} {{chem}} Markup
{{chem|Ba|2+}} + {{chem|S|O|4|2-}} → {{chem|Ba|S|O|4}}↓ Renders as
Ba2+
+ SO2−
4 → BaSO
4↓
{{chem2}} Markup
{{chem2|Ba(2+) + SO4(2-) -> BaSO4↓}} Renders as
Ba2+ + SO2−4 → BaSO4↓
Equivalent HTML MarkupBa<sup>2+</sup> + SO<sub>4</sub><sup>2−</sup> → BaSO<sub>4</sub>↓Ba2+ + SO42− → BaSO4↓
mhchem Markup<chem>2HCl + Zn -> ZnCl2 + H2 ^</chem>Renders as 2 HCl + Zn ⟶ ZnCl 2 + H 2 ↑ {\displaystyle {\ce {2HCl + Zn -> ZnCl2 + H2 ^}}}
Using postscript drivers may in some cases give smoother curves and will handle fonts differently:
Once you have produced your diagram in LaTeX (or TeX), you can convert it to an SVG file using the following sequence of commands:
The pdfcrop and pdf2svg utilities are needed for this procedure. You can alternatively use pdf2svg from PDFTron for the last step.
If you do not have pdfTeX (which is unlikely) you can use the following commands to replace the first step (TeX → PDF):
In general, you will not be able to get anywhere with diagrams without TeX and Ghostscript, and the inkscape program is a useful tool for creating or modifying your diagrams by hand. There is also a utility pstoedit which supports direct conversion from Postscript files to many vector graphics formats, but it requires a non-free plugin to convert to SVG, and regardless of the format, this editor has not been successful in using it to convert diagrams with diagonal arrows from TeX-created files.
As the diagram is your own work, upload it to Wikimedia Commons, so that all projects (notably, all languages) can use it without having to copy it to their language's Wiki. (If you've previously uploaded a file to somewhere other than Commons, to Commons.)
Now go to the image page and add a description, including the source code, using this template:
While links from formulas using LaTeX macros such as \href or \url or are currently not supported, one can link individual math expressions to Wikidata items to explain the meaning of individual terms of mathematical expressions. For example,
Markup<math qid=Q35875>E=mc^2</math>links to a special page that displays additional information on that formula. To change the information shown on the special page, navigate to the Wikidata item linked at the bottom of the special page. Use the has part property to link parts of the equation to other Wikidata items with their respective Wikipedia articles. This is not limited to individual identifiers, but can also be used to link more complex terms.
A condensed version of that special page might be shown in the future as a popup: phab:T239357.
Markup<math>ax^2 + bx + c = 0</math><math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math><math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</math><math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math><math>\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math><math>\int_e^{\infty}\frac {1}{t(\ln t)^2}dt = \left. \frac{-1}{\ln t} \right\vert_e^\infty = 1</math><math>\det(\mathsf{A}-\lambda\mathsf{I}) = 0</math><math>\sum_{i=0}^{n-1} i</math><math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2 n}{3^m\left(m 3^n + n 3^m\right)}</math><math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math><math>|\bar{z}| = |z|,
|(\bar{z})^n| = |z|^n,
\arg(z^n) = n \arg(z)</math>
<math>\lim_{z\to z_0} f(z)=f(z_0)</math><math>\phi_n(\kappa) =
\frac{1}{4\pi^2\kappa^2} \int_0^\infty
\frac{\sin(\kappa R)}{\kappa R}
\frac{\partial}{\partial R}
\left [ R^2\frac{\partial D_n(R)}{\partial R} \right ] \,dR</math>
<math>\phi_n(\kappa) =
0.033C_n^2\kappa^{-11/3},\quad
\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>
<math>f(x) =
\begin{cases}
1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\
1 - x^2 & \text{otherwise}
\end{cases}</math>
<math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
= \sum_{n=0}^\infty
\frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
\frac{z^n}{n!}</math>
<math>\frac{a}{b}\ \tfrac{a}{b}</math><math>S=dD\sin\alpha</math><math> V = \frac{1}{6} \pi h \left [ 3 \left ( r_1^2 + r_2^2 \right ) + h^2 \right ] </math>The altered newline code \\[0.6ex] below adds a vertical space between the two lines of length equal to 0.6 {\displaystyle 0.6} times the height of a single 'x' character.
<math>\begin{align}
u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\[0.6ex]
v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v)
\end{align}</math>
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