User:Jmkim dot com/TeX Samples

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TeX Samples
TeX 샘플

nowiki Test[edit]

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

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

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

Inequality Sign Test[edit]

<math>1<2</math>

<math>2>1</math>

<math>1\lt 2</math>

Failed to parse (unknown function "\lt"): {\displaystyle 1\lt 2}

<math>2\gt 1</math>

Failed to parse (unknown function "\gt"): {\displaystyle 2\gt 1}

Inequality Sign Test 2[edit]

<math>a<b</math>

<math>a < b</math>

<math>a>b</math>

<math>a > b</math>

UTF-8 Test[edit]

<math>전압 = 전류 \times 저항</math>

Failed to parse (syntax error): {\displaystyle 전압 = 전류 \times 저항}

<math>저항 = \frac{전압}{전류}</math>

Failed to parse (syntax error): {\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>

Failed to parse (syntax error): {\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?

개의 동전을 던져 앞면 가 나올 확률 는?

The Lorenz Equations[edit]

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

The Cauchy-Schwarz Inequality[edit]

<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>

A Cross Product Formula[edit]

<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>

The probability of getting k heads when flipping n coins is[edit]

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

An Identity of Ramanujan[edit]

<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>

A Rogers-Ramanujan Identity[edit]

<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})},
\quad\quad for\,|q|<1.</math>

Maxwell’s Equations[edit]

<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>

같이 보기[edit]

참고 자료[edit]