# User:Jmkim dot com/TeX Samples

TeX Samples
TeX 샘플

## nowiki Test

<math>E=mc^2</math>


${\displaystyle E=mc^{2}}$

<nowiki><math>E=mc^2</math></nowiki>


$E=mc^2$

## Inequality Sign Test

<math>1<2</math>


${\displaystyle 1<2}$

<math>2>1</math>


${\displaystyle 2>1}$

<math>1\lt 2</math>


$\displaystyle 1\lt 2$

<math>2\gt 1</math>


$\displaystyle 2\gt 1$

## Inequality Sign Test 2

<math>a<b</math>


${\displaystyle a

<math>a < b</math>


${\displaystyle a

<math>a>b</math>


${\displaystyle a>b}$

<math>a > b</math>


${\displaystyle a>b}$

${\displaystyle f(x)=1}$

## UTF-8 Test

<math>전압 = 전류 \times 저항</math>


$\displaystyle 전압 = 전류 \times 저항$

<math>저항 = \frac{전압}{전류}</math>


$\displaystyle 저항 = \frac{전압}{전류}$

<math>償還までの合計利回り =\left(1+\frac{期間利率}{100}\right)^{期間}</math>


$\displaystyle 償還までの合計利回り =\left(1+\frac{期間利率}{100}\right)^{期間}$

<math>n</math>개의 동전을 던져 앞면 <math>k</math>가 나올 확률 <math>P(E)</math>는?


${\displaystyle n}$개의 동전을 던져 앞면 ${\displaystyle k}$가 나올 확률 ${\displaystyle P(E)}$는?

## The Lorenz Equations

<math>\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}</math>


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

## The Cauchy-Schwarz Inequality

<math>\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)</math>


${\displaystyle \left(\sum _{k=1}^{n}a_{k}b_{k}\right)^{2}\leq \left(\sum _{k=1}^{n}a_{k}^{2}\right)\left(\sum _{k=1}^{n}b_{k}^{2}\right)}$

## A Cross Product Formula

<math>\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}</math>


${\displaystyle \mathbf {V} _{1}\times \mathbf {V} _{2}={\begin{vmatrix}\mathbf {i} &\mathbf {j} &\mathbf {k} \\{\frac {\partial X}{\partial u}}&{\frac {\partial Y}{\partial u}}&0\\{\frac {\partial X}{\partial v}}&{\frac {\partial Y}{\partial v}}&0\end{vmatrix}}}$

## The probability of getting k heads when flipping n coins is

<math>P(E)   = {n \choose k} p^k (1-p)^{ n-k}</math>


${\displaystyle P(E)={n \choose k}p^{k}(1-p)^{n-k}}$

## An Identity of Ramanujan

<math>\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} =
1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}}
{1+\frac{e^{-8\pi}} {1+\ldots} } } }</math>


${\displaystyle {\frac {1}{{\Bigl (}{\sqrt {\phi {\sqrt {5}}}}-\phi {\Bigr )}e^{{\frac {2}{5}}\pi }}}=1+{\frac {e^{-2\pi }}{1+{\frac {e^{-4\pi }}{1+{\frac {e^{-6\pi }}{1+{\frac {e^{-8\pi }}{1+\ldots }}}}}}}}}$

## A Rogers-Ramanujan Identity

<math>1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots
= \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},


${\displaystyle 1+{\frac {q^{2}}{(1-q)}}+{\frac {q^{6}}{(1-q)(1-q^{2})}}+\cdots =\prod _{j=0}^{\infty }{\frac {1}{(1-q^{5j+2})(1-q^{5j+3})}},\quad \quad for\,|q|<1.}$

## Maxwell’s Equations

<math>\begin{align}
\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{align}</math>


{\displaystyle {\begin{aligned}\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 {\mathbf {0} }}\\\nabla \cdot {\vec {\mathbf {B} }}&=0\end{aligned}}}