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博客园支持latex直接输入哦
$$\sum_{n=1}^{\infty}\frac{1}{n^s}=\prod_{p\in\mathcal{P}}\frac{1}{1-p^{-s}}.$$ The Cauchy-Schwarz Inequality\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
A Cross Product Formula
\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]
The probability of getting \(k\) heads when flipping \(n\) coins is:
\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]
An Identity of Ramanujan
\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]
\begin{equation}0.3x+y/2=4z\end{equation}
$$\beta$$
Hello, world! $\LaTeX$ can typeset equations like
\begin{equation}
\int^{2\pi}_0\sin^2\theta d\theta = \frac{1}{2}
\end{equation}
\begin{equation}
\left[
{\bf X} + {\rm a} \ \geq\
\underline{\hat a} \sum_i^N \lim_{x \rightarrow k} \delta C
\right]
\end{equation}
very cool!
\begin{equation}
0.3x+y/2=4z
\end{equation}
The Lorenz Equations
\[\begin{matrix} \dot{x} & = & \sigma(y-x) \\ \dot{y} & = & \rho x - y - xz \\ \dot{z} & = & -\beta z + xy \end{matrix} \]
博客园支持latex直接输入哦