Latex Ref [E]

Latex

Katex¹

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Doublestruck Letters

$\mathbb{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}$

$\mathbb{A}\mathbb{B}\mathbb{C}\mathbb{D}\mathbb{E}\mathbb{F}\mathbb{G}\mathbb{H}\mathbb{I}\mathbb{J}\mathbb{K}\mathbb{L}\mathbb{M}\mathbb{N}\mathbb{O}\mathbb{P}\mathbb{Q}\mathbb{R}\mathbb{S}\mathbb{T}\mathbb{U}\mathbb{V}\mathbb{W}\mathbb{X}\mathbb{Y}\mathbb{Z}$

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Repeating fractions

$\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }$

$\frac{1}{(\sqrt{\varphi \sqrt{5}}-\varphi )e^{\frac{2}{5}\pi }}\equiv 1+\frac{e^{-2\pi }}{1+\frac{e^{-4\pi }}{1+\frac{e^{-6\pi }}{1+\frac{e^{-8\pi }}{1+\cdots }}}}$

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Summation notation

$\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)$

${\left({\sum }_{k=1}^n{a}_k{b}_k\right)}^2\le \left({\sum }_{k=1}^n{a}_k^2\right)\left({\sum }_{k=1}^n{b}_k^2\right)$

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Sum of a Series

$\displaystyle\sum_{i=1}^{k+1}i$

$\sum _{i=1}^{k+1}i$

$\displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1)$

$=\left(\sum _{i=1}^{k}i\right)+(k+1)$

$\displaystyle= \frac{k(k+1)}{2}+k+1$

$=\frac{k(k+1)}{2}+k+1$

$\displaystyle= \frac{k(k+1)+2(k+1)}{2}$

$=\frac{k(k+1)+2(k+1)}{2}$

$\displaystyle= \frac{(k+1)(k+2)}{2}$

$=\frac{(k+1)(k+2)}{2}$

$\displaystyle= \frac{(k+1)((k+1)+1)}{2}$

$=\frac{(k+1)((k+1)+1)}{2}$

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Product notation

$\displaystyle\text{ for }\lvert q\rvert < 1.$

$\text{ for }|q|<1.$

$= \displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},$

$=\prod _{j=0}^{\infty }\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},$

$\displaystyle1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots$

$1+\frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots$

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Inline math²

<span class="math">...</span>

And $k_{n+1} = n^2 + k_n^2 - k_{n-1}$, text.

And $k_{n+1}=n^2+k_n^2-k_{n-1}$​, text.

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Greek Letters

$\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega$

$\Gamma \Delta \Theta \Lambda \Xi \Pi \Sigma {\rm Y}\Phi \Psi \Omega$

$\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi\ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega$

$\alpha \beta \gamma \delta ϵ\zeta \eta \theta \iota \kappa \lambda \mu \nu \xi o\pi \rho \sigma \tau \upsilon \varphi \chi \psi \omega$

$\varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi$

$\epsilon \vartheta \varpi \varrho \varsigma \phi$

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Arrows

$\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow$

$\leftarrow \to \leftarrow \to \uparrow \Uparrow \downarrow \Downarrow \updownarrow \Updownarrow$

$\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow$

$\Leftarrow \Rightarrow \leftrightarrow \iff \mapsto \hookleftarrow$

$\leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow$

$\leftharpoonup \leftharpoondown \rightleftharpoons ⟵⟸⟶$

$\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup$

$⟹⟷⟺⟼\hookrightarrow \rightharpoonup$

LaTeX code:
$\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow$

$\rightharpoondown ⇝\nearrow \searrow \swarrow \nwarrow$

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Symbols

$\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup$

$\surd ⊼⊻\odot \oplus \otimes \oslash ⊚⊡△$

$\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle$

$▽†\diamond \star ◃▹\angle \infty \prime △$

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Calculus

$\int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx$

$\int u\frac{dv}{dx}dx=uv-\int \frac{du}{dx}vdx$

$f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x}$

$f(x)={\int }_{-\infty }^{\infty }\hat{f}(\xi )e^{2\pi i\xi x}$

$\oint \vec{F} \cdot d\vec{s}=0$

$\oint \vec{F}\cdot d\vec{s}=0$

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Lorenz Equations

$\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned}$

$\begin{array}{rl}\dot{x}& =\sigma (y-x)\\ \dot{y}& =\rho x-y-xz\\ \dot{z}& =-\beta z+xy\end{array}$

Cross Product

$\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix}$

${\mathbf{V}}_1\times {\mathbf{V}}_2=\left|\begin{array}{ccc}\mathbf{i}& \mathbf{j}& \mathbf{k}\\ \frac{\partial X}{\partial u}& \frac{\partial Y}{\partial u}& 0\\ \frac{\partial X}{\partial v}& \frac{\partial Y}{\partial v}& 0\end{array}\right|$

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Accents

$\hat{x}\ \vec{x}\ \ddot{x}$

$\hat{x}\vec{x}\ddot{x}$

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Stretchy brackets

$\left(\frac{x^2}{y^3}\right)$

$\left(\frac{x^2}{y^3}\right)$

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Evaluation at limits

$\left.\frac{x^3}{3}\right|_0^1$

${\frac{x^3}{3}|}_0^1$

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Case definitions

$f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases}$

$f(n)=\{\begin{array}{ll}\frac{n}{2},& \text{if }n\text{ is even}\\ 3n+1,& \text{if }n\text{ is odd}\end{array}$

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Maxwell’s Equations

$\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}$

$\begin{array}{rl}\nabla \times \vec{\mathbf{B}}-\frac{1}{c}\frac{\partial \vec{\mathbf{E}}}{\partial t}& =\frac{4\pi }{c}\vec{\mathbf{j}}\\ \nabla \cdot \vec{\mathbf{E}}& =4\pi \rho \\ \nabla \times \vec{\mathbf{E}}+\frac{1}{c}\frac{\partial \vec{\mathbf{B}}}{\partial t}& =\vec{0}\\ \nabla \cdot \vec{\mathbf{B}}& =0\end{array}$

$\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\[1em] \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\[0.5em] \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\[1em] \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}$

$\begin{array}{rl}\nabla \times \vec{\mathbf{B}}-\frac{1}{c}\frac{\partial \vec{\mathbf{E}}}{\partial t}& =\frac{4\pi }{c}\vec{\mathbf{j}}\\ \nabla \cdot \vec{\mathbf{E}}& =4\pi \rho \\ \nabla \times \vec{\mathbf{E}}+\frac{1}{c}\frac{\partial \vec{\mathbf{B}}}{\partial t}& =\vec{0}\\ \nabla \cdot \vec{\mathbf{B}}& =0\end{array}$

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Statistics

$\frac{n!}{k!(n-k)!} = {^n}C_k$

$\frac{n!}{k!(n-k)!}={}^n{C}_k$

${n \choose k}$

$\left(\genfrac{}{}{0ex}{}{n}{k}\right)$

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Fractions on fractions

$\frac{\frac{1}{x}+\frac{1}{y}}{y-z}$

$\frac{\frac{1}{x}+\frac{1}{y}}{y-z}$

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n-th root

$\sqrt[n]{1+x+x^2+x^3+\ldots}$

$\sqrt[n]{1+x+x^2+x^3+\dots }$

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Matrices

$\begin{pmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{pmatrix}$

$\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right)$

$begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}$

$\left[\begin{array}{ccc}0& \cdots & 0\\ ⋮& \ddots & ⋮\\ 0& \cdots & 0\end{array}\right]$

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Punctuation

$(x) = \sqrt{1+x} \quad (x \ge -1)$

$f(x)=\sqrt{1+x}(x\ge -1)$

$f(x) \sim x^2 \quad (x\to\infty)$

$f(x)\sim x^2(x\to \infty )$

$f(x) = \sqrt{1+x}, \quad x \ge -1$

$f(x)=\sqrt{1+x},x\ge -1$

$f(x) \sim x^2, \quad x\to\infty$

$f(x)\sim x^2,x\to \infty$

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$\Gamma$ function

$\Gamma(n) = (n-1)!\quad\forall n\in\mathbb N$

$\Gamma (n)=(n-1)!\forall n\in \mathbb{N}$

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Euler integral

$\Gamma(z) = \int_0^\infty t^{z-1}e^{-t}dt\,.$

$\Gamma (z)={\int }_0^{\infty }{t}^{z-1}{e}^{-t}dt.$

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1. katext - ref ↩︎

2. Elaboration needed ↩︎