博客中Markdown公式编辑问题

21 Nov 2013

Categories: Technique     Tags: markdown, latex, github-pages

利用MathJax渲染 每个页面开头加这么一句话：

测试一下

The Lorentz Equations

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

The Cauchy-Schwarz Inequality

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

A Cross Product Formula

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

The probability of getting k heads when flipping n coins is

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

An Identity of Ramanujan

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

A Rogers-Ramanujan Identity

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

Maxwell’s Equations

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

使用过程不知道会不会有bug，日后有碰到再补上。
PS：如果用hexo，发现hexo-math蛮好用的。