Maths

Functions, symbols, special characters

Accents/Diacritics
\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}	<math>\acute{a} \grave{a} \hat{a} \tilde{a} \breve{a}\,\!</math>
\check{a} \bar{a} \ddot{a} \dot{a}	<math>\check{a} \bar{a} \ddot{a} \dot{a}\,\!</math>
Standard functions
\sin a \cos b \tan c	<math>\sin a \cos b \tan c\,\!</math>
\sec d \csc e \cot f	<math>\sec d \csc e \cot f\,\!</math>
\arcsin h \arccos i \arctan j	<math>\arcsin h \arccos i \arctan j\,\!</math>
\sinh k \cosh l \tanh m \coth n	<math>\sinh k \cosh l \tanh m \coth n\,\!</math>
\operatorname{sh}o \operatorname{ch}p \operatorname{th}q	<math>\operatorname{sh}o \operatorname{ch}p \operatorname{th}q\,\!</math>
\operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t	<math>\operatorname{argsh}r \operatorname{argch}s \operatorname{argth}t\,\!</math>
\lim u \limsup v \liminf w \min x \max y	<math>\lim u \limsup v \liminf w \min x \max y\,\!</math>
\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g	<math>\inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g\,\!</math>
\deg h \gcd i \Pr j \det k \hom l \arg m \dim n	<math>\deg h \gcd i \Pr j \det k \hom l \arg m \dim n\,\!</math>
Modular arithmetic
s_k \equiv 0 \pmod{m} a \bmod b	<math>s_k \equiv 0 \pmod{m} a \bmod b\,\!</math>
Derivatives
\nabla \partial x dx \dot x \ddot y	<math>\nabla \partial x dx \dot x \ddot y\,\!</math>
Sets
\forall \exists \empty \emptyset \varnothing	<math>\forall \exists \empty \emptyset \varnothing\,\!</math>
\in \ni \not \in \notin \subset \subseteq \subsetneq \supset \supseteq \supsetneq	<math>\in \ni \not \in \notin \subset \subseteq \subsetneq \supset \supseteq \supsetneq\,\!</math>
\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	<math>\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\!</math>
\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup	<math>\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\!</math>
Operators
+ \oplus \bigoplus \pm \mp -	<math>+ \oplus \bigoplus \pm \mp - \,\!</math>
\times \otimes \bigotimes \cdot \circ \bullet \bigodot	<math>\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\!</math>
\star * / \div \frac{1}{2}	<math>\star * / \div \frac{1}{2}\,\!</math>
Logic
\land \wedge \bigwedge \bar{q} \to p	<math>\land \wedge \bigwedge \bar{q} \to p\,\!</math>
\lor \vee \bigvee \lnot \neg q \And	<math>\lor \vee \bigvee \lnot \neg q \And\,\!</math>
Root
\sqrt{2} \sqrt[n]{x}	<math>\sqrt{2} \sqrt[n]{x}\,\!</math>
Relations
\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}	<math>\sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=}\,\!</math>
\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto	<math>\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto\,\!</math>
Geometric
\Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ	45^\circ\,\!</math>
Arrows
\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow	<math>\leftarrow \gets \rightarrow \to \not\to \leftrightarrow \longleftarrow \longrightarrow\,\!</math>
\mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow	<math>\mapsto \longmapsto \hookrightarrow \hookleftarrow \nearrow \searrow \swarrow \nwarrow\,\!</math>
\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft	<math>\uparrow \downarrow \updownarrow \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft\,\!</math>
\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow	<math>\upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow\,\!</math>
\Longrightarrow \Longleftrightarrow (or \iff) \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft	<math>\Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!</math>
\leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright	<math>\leftrightharpoons \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright\,\!</math>
\curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow	<math>\curvearrowright \circlearrowright \Rsh \downdownarrows \multimap \leftrightsquigarrow \rightsquigarrow \nLeftarrow \nleftrightarrow \nRightarrow\,\!</math>
\nLeftrightarrow \longleftrightarrow	<math>\nLeftrightarrow \longleftrightarrow\,\!</math>
Special
\eth \S \P \% \dagger \ddagger \ldots \cdots	<math>\eth \S \P \% \dagger \ddagger \ldots \cdots\,\!</math>
\smile \frown \wr \triangleleft \triangleright \infty \bot \top	<math>\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\!</math>
\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar	<math>\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\!</math>
\ell \mho \Finv \Re \Im \wp \complement \diamondsuit	<math>\ell \mho \Finv \Re \Im \wp \complement \diamondsuit\,\!</math>
\heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp	<math>\heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\!</math>
Unsorted (new stuff)
\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown	<math> \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown</math>
\blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge	<math> \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge</math>
\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes	<math> \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes</math>
\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant	<math> \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant</math>
\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq	<math> \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq</math>
\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft	<math> \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft</math>
\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot	<math> \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot</math>
\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq	<math> \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq</math>
\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork	<math> \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork</math>
\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq	<math> \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq</math>
\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid	<math> \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid</math>
\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr	<math> \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr</math>
\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq	<math> \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq</math>
\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq	<math> \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq</math>
\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq	<math> \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq</math>
\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus	<math>\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\!</math>
\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq	<math>\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\!</math>
\dashv \asymp \doteq \parallel	<math>\dashv \asymp \doteq \parallel\,\!</math>

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
		HTML	PNG
Superscript	a^2	<math>a^2</math>	<math>a^2 \,\!</math>
Subscript	a_2	<math>a_2</math>	<math>a_2 \,\!</math>
Grouping	a^{2+2}	<math>a^{2+2}</math>	<math>a^{2+2}\,\!</math>
	a_{i,j}	<math>a_{i,j}</math>	<math>a_{i,j}\,\!</math>
Combining sub & super	x_2^3	<math>x_2^3</math>
Preceding and/or Additional sub & super	\sideset{_1^2}{_3^4}\prod_a^b	<math>\sideset{_1^2}{_3^4}\prod_a^b</math>
	{}_1^2\!\Omega_3^4	<math>{}_1^2\!\Omega_3^4</math>
Stacking	\overset{\alpha}{\omega}	<math>\overset{\alpha}{\omega}</math>
	\underset{\alpha}{\omega}	<math>\underset{\alpha}{\omega}</math>
	\overset{\alpha}{\underset{\gamma}{\omega}}	<math>\overset{\alpha}{\underset{\gamma}{\omega}}</math>
	\stackrel{\alpha}{\omega}	<math>\stackrel{\alpha}{\omega}</math>
Derivative (forced PNG)	x', y'', f', f''\!		<math>x', y, f', f\!</math>
Derivative (f in italics may overlap primes in HTML)	x', y'', f', f''	<math>x', y, f', f</math>	<math>x', y, f', f\!</math>
Derivative (wrong in HTML)	x^\prime, y^{\prime\prime}	<math>x^\prime, y^{\prime\prime}</math>	<math>x^\prime, y^{\prime\prime}\,\!</math>
Derivative (wrong in PNG)	x\prime, y\prime\prime	<math>x\prime, y\prime\prime</math>	<math>x\prime, y\prime\prime\,\!</math>
Derivative dots	\dot{x}, \ddot{x}	<math>\dot{x}, \ddot{x}</math>
Underlines, overlines, vectors	\hat a \ \bar b \ \vec c	<math>\hat a \ \bar b \ \vec c</math>
	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}	<math>\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}</math>
	\overline{g h i} \ \underline{j k l}	<math>\overline{g h i} \ \underline{j k l}</math>
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	<math> A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</math>
Overbraces	\overbrace{ 1+2+\cdots+100 }^{5050}	<math>\overbrace{ 1+2+\cdots+100 }^{5050}</math>
Underbraces	\underbrace{ a+b+\cdots+z }_{26}	<math>\underbrace{ a+b+\cdots+z }_{26}</math>
Sum	\sum_{k=1}^N k^2	<math>\sum_{k=1}^N k^2</math>
Sum (force \textstyle)	\textstyle \sum_{k=1}^N k^2	<math>\textstyle \sum_{k=1}^N k^2</math>
Product	\prod_{i=1}^N x_i	<math>\prod_{i=1}^N x_i</math>
Product (force \textstyle)	\textstyle \prod_{i=1}^N x_i	<math>\textstyle \prod_{i=1}^N x_i</math>
Coproduct	\coprod_{i=1}^N x_i	<math>\coprod_{i=1}^N x_i</math>
Coproduct (force \textstyle)	\textstyle \coprod_{i=1}^N x_i	<math>\textstyle \coprod_{i=1}^N x_i</math>
Limit	\lim_{n \to \infty}x_n	<math>\lim_{n \to \infty}x_n</math>
Limit (force \textstyle)	\textstyle \lim_{n \to \infty}x_n	<math>\textstyle \lim_{n \to \infty}x_n</math>
Integral	\int_{-N}^{N} e^x\, dx	<math>\int_{-N}^{N} e^x\, dx</math>
Integral (force \textstyle)	\textstyle \int_{-N}^{N} e^x\, dx	<math>\textstyle \int_{-N}^{N} e^x\, dx</math>
Double integral	\iint_{D}^{W} \, dx\,dy	<math>\iint_{D}^{W} \, dx\,dy</math>
Triple integral	\iiint_{E}^{V} \, dx\,dy\,dz	<math>\iiint_{E}^{V} \, dx\,dy\,dz</math>
Quadruple integral	\iiiint_{F}^{U} \, dx\,dy\,dz\,dt	<math>\iiiint_{F}^{U} \, dx\,dy\,dz\,dt</math>
Path integral	\oint_{C} x^3\, dx + 4y^2\, dy	<math>\oint_{C} x^3\, dx + 4y^2\, dy</math>
Intersections	\bigcap_1^{n} p	<math>\bigcap_1^{n} p</math>
Unions	\bigcup_1^{k} p	<math>\bigcup_1^{k} p</math>

Fractions, matrices, multilines

Feature	Syntax	How it looks rendered
Fractions	\frac{2}{4}=0.5	<math>\frac{2}{4}=0.5</math>
Small Fractions	\tfrac{2}{4} = 0.5	<math>\tfrac{2}{4} = 0.5</math>
Large (normal) Fractions	\dfrac{2}{4} = 0.5	<math>\dfrac{2}{4} = 0.5</math>
Large (nestled) Fractions	\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a	<math>\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a</math>
Binomial coefficients	\binom{n}{k}	<math>\binom{n}{k}</math>
Small Binomial coefficients	\tbinom{n}{k}	<math>\tbinom{n}{k}</math>
Large (normal) Binomial coefficients	\dbinom{n}{k}	<math>\dbinom{n}{k}</math>
Matrices	\begin{matrix} x & y \\ z & v \end{matrix}	<math>\begin{matrix} x & y \\ z & v \end{matrix}</math>
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	<math>\begin{vmatrix} x & y \\ z & v \end{vmatrix}</math>
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	<math>\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}</math>
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}	<math>\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} </math>
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	<math>\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}</math>
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	<math>\begin{pmatrix} x & y \\ z & v \end{pmatrix}</math>
	\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)	<math> \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) </math>
Case distinctions	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}	<math>f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases} </math>
Multiline equations	\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}	<math> \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} </math>
	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}	<math> \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} </math>
Multiline equations (must define number of colums used ({lcr}) (should not be used unless needed)	\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	<math>\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>
Multiline equations (more)	\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}	<math>\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}</math>
Breaking up a long expression so that it wraps when necessary	<math>f(x) \,\!</math> <math>= \sum_{n=0}^\infty a_n x^n </math> <math>= a_0+a_1x+a_2x^2+\cdots</math>	<math>f(x) \,\!</math><math>= \sum_{n=0}^\infty a_n x^n </math><math>= a_0 +a_1x+a_2x^2+\cdots</math>
Simultaneous equations	\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}	<math>\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}</math>

Alphabets and typefaces

Greek alphabet
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta	<math>\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\!</math>
\Eta \Theta \Iota \Kappa \Lambda \Mu	<math>\Eta \Theta \Iota \Kappa \Lambda \Mu \,\!</math>
\Nu \Xi \Pi \Rho \Sigma \Tau	<math>\Nu \Xi \Pi \Rho \Sigma \Tau\,\!</math>
\Upsilon \Phi \Chi \Psi \Omega	<math>\Upsilon \Phi \Chi \Psi \Omega \,\!</math>
\alpha \beta \gamma \delta \epsilon \zeta	<math>\alpha \beta \gamma \delta \epsilon \zeta \,\!</math>
\eta \theta \iota \kappa \lambda \mu	<math>\eta \theta \iota \kappa \lambda \mu \,\!</math>
\nu \xi \pi \rho \sigma \tau	<math>\nu \xi \pi \rho \sigma \tau \,\!</math>
\upsilon \phi \chi \psi \omega	<math>\upsilon \phi \chi \psi \omega \,\!</math>
\varepsilon \digamma \vartheta \varkappa	<math>\varepsilon \digamma \vartheta \varkappa \,\!</math>
\varpi \varrho \varsigma \varphi	<math>\varpi \varrho \varsigma \varphi\,\!</math>
Blackboard Bold/Scripts
\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G}	<math>\mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} \,\!</math>
\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M}	<math>\mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} \,\!</math>
\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T}	<math>\mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} \,\!</math>
\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}	<math>\mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z}\,\!</math>
boldface (vectors)
\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G}	<math>\mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} \,\!</math>
\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M}	<math>\mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} \,\!</math>
\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T}	<math>\mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} \,\!</math>
\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z}	<math>\mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} \,\!</math>
\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g}	<math>\mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} \,\!</math>
\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m}	<math>\mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} \,\!</math>
\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t}	<math>\mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} \,\!</math>
\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z}	<math>\mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} \,\!</math>
\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4}	<math>\mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} \,\!</math>
\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}	<math>\mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9}\,\!</math>
Boldface (greek)
\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta}	<math>\boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} \,\!</math>
\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}	<math>\boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu}\,\!</math>
\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}	<math>\boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau}\,\!</math>
\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}	<math>\boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega}\,\!</math>
\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}	<math>\boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta}\,\!</math>
\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}	<math>\boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu}\,\!</math>
\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}	<math>\boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau}\,\!</math>
\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}	<math>\boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega}\,\!</math>
\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa}	<math>\boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} \,\!</math>
\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}	<math>\boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi}\,\!</math>
Italics
\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G}	<math>\mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} \,\!</math>
\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M}	<math>\mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} \,\!</math>
\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T}	<math>\mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} \,\!</math>
\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z}	<math>\mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} \,\!</math>
\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g}	<math>\mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} \,\!</math>
\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m}	<math>\mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} \,\!</math>
\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t}	<math>\mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} \,\!</math>
\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z}	<math>\mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} \,\!</math>
\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4}	<math>\mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} \,\!</math>
\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}	<math>\mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9}\,\!</math>
Roman typeface
\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G}	<math>\mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} \,\!</math>
\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M}	<math>\mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} \,\!</math>
\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T}	<math>\mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} \,\!</math>
\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z}	<math>\mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} \,\!</math>
\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}	<math>\mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g}\,\!</math>
\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m}	<math>\mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} \,\!</math>
\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t}	<math>\mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} \,\!</math>
\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z}	<math>\mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} \,\!</math>
\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4}	<math>\mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} \,\!</math>
\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}	<math>\mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9}\,\!</math>
Fraktur typeface
\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G}	<math>\mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} \,\!</math>
\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M}	<math>\mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} \,\!</math>
\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T}	<math>\mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} \,\!</math>
\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z}	<math>\mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} \,\!</math>
\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g}	<math>\mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} \,\!</math>
\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m}	<math>\mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} \,\!</math>
\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t}	<math>\mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} \,\!</math>
\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z}	<math>\mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} \,\!</math>
\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4}	<math>\mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} \,\!</math>
\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}	<math>\mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9}\,\!</math>
Calligraphy/Script
\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G}	<math>\mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} \,\!</math>
\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M}	<math>\mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} \,\!</math>
\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T}	<math>\mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} \,\!</math>
\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}	<math>\mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z}\,\!</math>
Hebrew
\aleph \beth \gimel \daleth	<math>\aleph \beth \gimel \daleth\,\!</math>

Feature	Syntax	How it looks rendered
non-italicised characters	\mbox{abc}	<math>\mbox{abc}</math>	<math>\mbox{abc} \,\!</math>
mixed italics (bad)	\mbox{if} n \mbox{is even}	<math>\mbox{if} n \mbox{is even}</math>	<math>\mbox{if} n \mbox{is even} \,\!</math>
mixed italics (good)	\mbox{if }n\mbox{ is even}	<math>\mbox{if }n\mbox{ is even}</math>	<math>\mbox{if }n\mbox{ is even} \,\!</math>
mixed italics (more legible: ~ is a non-breaking space, while "\ " forces a space)	\mbox{if}~n\ \mbox{is even}	<math>\mbox{if}~n\ \mbox{is even}</math>	<math>\mbox{if}~n\ \mbox{is even} \,\!</math>

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Bad	( \frac{1}{2} )	<math>( \frac{1}{2} )</math>
Good	\left ( \frac{1}{2} \right )	<math>\left ( \frac{1}{2} \right )</math>

You can use various delimiters with \left and \right:

Feature	Syntax	How it looks rendered
Parentheses	\left ( \frac{a}{b} \right )	<math>\left ( \frac{a}{b} \right )</math>
Brackets	\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack	<math>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</math>
Braces	\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace	<math>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</math>
Angle brackets	\left \langle \frac{a}{b} \right \rangle	<math>\left \langle \frac{a}{b} \right \rangle</math>
Bars and double bars	\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|	<math>\left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \|</math>
Floor and ceiling functions:	\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil	<math>\left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil</math>
Slashes and backslashes	\left / \frac{a}{b} \right \backslash	<math>\left / \frac{a}{b} \right \backslash</math>
Up, down and up-down arrows	\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow	<math>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</math>
Delimiters can be mixed, as long as \left and \right match	\left [ 0,1 \right ) \left \langle \psi \right |	<math>\left [ 0,1 \right )</math> <math>\left \langle \psi \right |</math>
Use \left. and \right. if you don't want a delimiter to appear:	\left . \frac{A}{B} \right \} \to X	<math>\left . \frac{A}{B} \right \} \to X</math>
Size of the delimiters	\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]	<math>\big( \Big( \bigg( \Bigg( ... \Bigg] \bigg] \Big] \big]</math>
	\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle	<math>\big\{ \Big\{ \bigg\{ \Bigg\{ ... \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle</math>
	\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|	<math>\big\| \Big\| \bigg\| \Bigg\| ... \Bigg| \bigg| \Big| \big|</math>
	\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil	<math>\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor ... \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil</math>
	\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow	<math>\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow ... \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow</math>
	\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow	<math>\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow ... \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow</math>
	\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash	<math>\big / \Big / \bigg / \Bigg / ... \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash</math>

Spacing

Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Feature	Syntax	How it looks rendered
double quad space	a \qquad b	<math>a \qquad b</math>
quad space	a \quad b	<math>a \quad b</math>
text space	a\ b	<math>a\ b</math>
text space without PNG conversion	a \mbox{ } b	<math>a \mbox{ } b</math>
large space	a\;b	<math>a\;b</math>
medium space	a\>b	[not supported]
small space	a\,b	<math>a\,b</math>
no space	ab	<math>ab\,</math>
small negative space	a\!b	<math>a\!b</math>

Align with normal text flow

Due to the default css

img.tex { vertical-align: middle; }

an inline expression like <math>\int_{-N}^{N} e^x\, dx = 2 \sinh N</math> should look good.

If you need to align it otherwise, use <font style="vertical-align:-100%;"><math>...</math></font> 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.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

Forced PNG rendering

To force the formula to render as PNG, add \, (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in preferences).

You can also use \,\! (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike \,.

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

Syntax	How it looks rendered
a^{c+2}	<math>a^{c+2}</math>
a^{c+2} \,	<math>a^{c+2} \,</math>
a^{\,\!c+2}	<math>a^{\,\!c+2}</math>
a^{b^{c+2}}	<math>a^{b^{c+2}}</math> (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}} \,	<math>a^{b^{c+2}} \,</math> (WRONG with option "HTML if possible or else PNG"!)
a^{b^{c+2}}\approx 5	<math>a^{b^{c+2}}\approx 5</math> (due to "<math>\approx</math>" correctly displayed, no code "\,\!" needed)
a^{b^{\,\!c+2}}	<math>a^{b^{\,\!c+2}}</math>
\int_{-N}^{N} e^x\, dx	<math>\int_{-N}^{N} e^x\, dx</math>

This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->

Color

Equations can use color:

• {\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}

  <math>{\color{Blue}x^2}+{\color{Brown}2x}-{\color{OliveGreen}1}</math>

• x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}

  <math>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</math>

See here for all named colours supported by LaTeX.

Examples

Quadratic Polynomial

<math>ax^2 + bx + c = 0</math>

<math>ax^2 + bx + c = 0</math>

Quadratic Polynomial (Force PNG Rendering)

<math>ax^2 + bx + c = 0\,\!</math>

<math>ax^2 + bx + c = 0\,\!</math>

Quadratic Formula

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

Tall Parentheses and Fractions

<math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</math>

<math>2 = \left(
 \frac{\left(3-x\right) \times 2}{3-x}
 \right)</math>

<math>S_{new} = S_{old} + \frac{ \left( 5-T \right) ^2} {2}</math>

<math>S_{new} = S_{old} +
 \frac{ \left( 5-T \right) ^2} {2}</math>

Integrals

<math>\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>

<math>\int_a^x \int_a^s f(y)\,dy\,ds
 = \int_a^x f(y)(x-y)\,dy</math>

Summation

<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>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}</math>

Differential Equation

<math>u + p(x)u' + q(x)u=f(x),\quad x>a</math>

<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

Complex numbers

<math>|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)</math>

<math>|\bar{z}| = |z|,
 |(\bar{z})^n| = |z|^n,
 \arg(z^n) = n \arg(z)</math>

Limits

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

Integral Equation

<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) =
 \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>

Example

<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>\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

Continuation and cases

<math>f(x) = \begin{cases}1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\ 1 - x^2 & 0 < x \le 1\end{cases}</math>

<math>
 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & 0 < x\le 1
 \end{cases}
 </math>

Prefixed subscript

<math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}</math>

 <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}
 \frac{z^n}{n!}</math>