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The courageous Spaceman Spiff, interplanetary explorer extraordinare, lands on yet another bizarre planet!

\[\begin{align*}&\frac{\partial u}{\partial t}(x,t)=\beta \frac{\partial^{2}u}{\partial x^{2}}(x,t)\text{ ?!?}&\sum\limits^{\infty}_{n=1}c_{n}e^{-\beta(\frac{n\pi}{L})^{2}t}\sin(\frac{n\pi}{L}x)\text{ !?!}\\ &\mathscr{L}\{f\}(s)=\int_{0}^{\infty} e^{-s t} f(t)dt\text{ !?!?!}&\Gamma(z)=\int_0^{\infty} t^{z-1} e^{-t} d t\text{ ?!?!?}\end{align*}\]

There seems to be some consistency between the strange symbols, but our hero will have to dig deeper to uncover what they mean