MathJax v3 beta: MathML input, HTML output test

When $a \neq 0$ , there are two solutions to $a x^{2} + b x + c = 0$ and they are $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} .$

The Lorenz Equations

\begin{aligned} \dot{x} & = σ (y - x) \\ \dot{y} & = ρ x - y - x z \\ \dot{z} & = - β z + x y \end{aligned}

The Cauchy-Schwarz Inequality

{(\sum_{k = 1}^{n} a_{k} b_{k})}^{2} \leq (\sum_{k = 1}^{n} a_{k}^{2}) (\sum_{k = 1}^{n} b_{k}^{2})

A Cross Product Formula

V_{1} \times V_{2} = | \begin{matrix} i & j & k \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{matrix} |

The probability of getting $k$ heads when flipping $n$ coins is:

P (E) = (\binom{n}{k}) p^{k} (1 - p)^{n - k}

An Identity of Ramanujan

\frac{1}{(\sqrt{ϕ \sqrt{5}} - ϕ) e^{\frac{2}{5} π}} = 1 + \frac{e^{- 2 π}}{1 + \frac{e^{- 4 π}}{1 + \frac{e^{- 6 π}}{1 + \frac{e^{- 8 π}}{1 + \dots}}}}

A Rogers-Ramanujan Identity

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

Maxwell's Equations

\begin{aligned} \nabla \times \vec{B} - \frac{1}{c} \frac{\partial \vec{E}}{\partial t} & = \frac{4 π}{c} \vec{j} \\ \nabla \cdot \vec{E} & = 4 π ρ \\ \nabla \times \vec{E} + \frac{1}{c} \frac{\partial \vec{B}}{\partial t} & = \vec{0} \\ \nabla \cdot \vec{B} & = 0 \end{aligned}

In-line Mathematics

Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression $\sqrt{3 x - 1} + (1 + x)^{2}$ is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.