Text to test Katex automatic rendering of math in a page.

Content in inline mode: \(\alpha_{n+1} = n^2 + \alpha_n^2 - \alpha_{n-1}\)

And below, some in display mode:

\[ \begin{aligned} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{aligned} \] \[ \int u \frac{dv}{dx}\,dx = uv-\int \frac{du}{dx}v\,dx \]