LaTeXML Tests

Cauchy Shwartz 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) | (∑k=1 n a k b k)2≤(∑k=1 n a k 2)(∑k=1 n b k 2)
Cross Product
\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} | 𝐕 1×𝐕 2=|𝐢 𝐣 𝐤∂X∂u∂Y∂u 0∂X∂v∂Y∂v 0|
Lorenz Eqautions
\begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} | x˙=σ(y−x)y˙=ρ x−y−x z z˙=−β z+x y
Maxwell 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} | ∇×𝐁→−1 c∂𝐄→∂t=4 π c 𝐣→∇⋅𝐄→=4 π ρ∇×𝐄→+1 c∂𝐁→∂t=𝟎→∇⋅𝐁→=0
N Choose K
P(E) = \binom{n}{k} p^k (1-p)^{ n-k} \ | P(E)=(n k)p k(1−p)n−k
Ramanujan Identity
\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} } } } | 1(ϕ 5−ϕ)e 25 π=1+e−2 π 1+e−4 π 1+e−6 π 1+e−8 π 1+…
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. | 1+q 2(1−q)+q 6(1−q)(1−q 2)+⋯=∏j=0∞1(1−q 5 j+2)(1−q 5 j+3),for|q|<1.