Sandbox

$$\newcommand{E}[2]{#1_{\mathrm{#2}}}$$ $ \newcommand{\blah}{\alpha\beta} $ $ \newcommand{\blaha}{\alpha\beta} $ $ \newcommand{\blahb}{\alpha\beta} $ $ \newcommand{\blahc}{\alpha\beta} $ $ \newcommand{\blahd}{\alpha\beta} $ There is $ \frac{g \beta \Delta T H^3}{\alpha \nu} $ and then there is \[ \frac{g \beta \Delta T H^3}{\alpha \nu} \]

$ \begin{align} \frac{g \beta \Delta T H^3}{\alpha \nu} \end{align} $

\[ \begin{align} \frac{g \beta \Delta T H^3}{\alpha \nu} \end{align} \]

$ \blah $

$ \int_{-\infty}^{\infty}x(\tau)\,h(t-\tau)\,d\tau $