I'm looking to familiarize myself with the inverse Mellin transform \begin{align*} \mathcal{M}^{-1}[\varphi](t) = \frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty} t^{-s}\varphi(s)\, \mathrm{d}s \end{align*} I hope I'm not alone in finding it somewhat difficult to ascribe meaning to this formula, and hence wanted to practice it a bit by computing the very easiest inverse Mellin transforms.

What are the easiest inverse Mellin transforms to compute by hand?


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