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<math>1 + \frac{q^2}{(1-q)} + \frac{q^6}{(1-q)(1-q^2)} + \cdots | <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})}, | = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, | ||
\quad\quad for\,|q| | \quad\quad for\,|q|\lt 1.</math> | ||
== Maxwell의 방정식 == | == Maxwell의 방정식 == | ||
2014년 9월 10일 (수) 19:34 판
- TeX Samples
- TeX 샘플
1 UTF-8 테스트
<math>전압 = 전류 \times 저항</math>
[math]\displaystyle{ 전압 = 전류 \times 저항 }[/math]
<math>저항 = \frac{전압}{전류}</math>
[math]\displaystyle{ 저항 = \frac{전압}{전류} }[/math]
<math>償還までの合計利回り =\big(1+\frac{期間利率}{100}\big)^{期間}</math>
[math]\displaystyle{ 償還までの合計利回り =\big(1+\frac{期間利率}{100}\big)^{期間} }[/math]
<math>n</math>개의 동전을 던져 앞면 <math>k</math>가 나올 확률 <math>P(E)</math>는?
[math]\displaystyle{ n }[/math]개의 동전을 던져 앞면 [math]\displaystyle{ k }[/math]가 나올 확률 [math]\displaystyle{ P(E) }[/math]는?
2 Lorenz 방정식
<math>\begin{align}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{align}</math>
[math]\displaystyle{ \begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align} }[/math]
3 Cauchy-Schwarz 부등식
<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>
[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) }[/math]
4 벡터곱 공식
<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>
[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} }[/math]
5 [math]\displaystyle{ n }[/math]개의 동전을 던져 앞면 [math]\displaystyle{ k }[/math]가 나올 확률
<math>P(E) = {n \choose k} p^k (1-p)^{ n-k}</math>
[math]\displaystyle{ P(E) = {n \choose k} p^k (1-p)^{ n-k} }[/math]
6 Ramanujan의 항등식
<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>
[math]\displaystyle{ \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]
7 Rogers-Ramanujan 항등식
<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>
[math]\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|\lt 1. }[/math]
8 Maxwell의 방정식
<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>
[math]\displaystyle{ \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]
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