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Mathematica and WolframAlpha both indicate $$ \mathcal{M}_{s}^{-1}\left[\Gamma\left(1 + {\rm i}s\right)\right]\left(x\right) = -\,{\rm i} \operatorname{G}_{\,0,1}^{\,1,0}\,\left(x,{\rm i}\, \left\vert\, 1 \right.\,\right),\quad \Im\left(s\right) < 1 $$ but the parameters for the Meijer-G function seem to be invalid.


Question: What is the inverse Mellin Transform of $\ \Gamma\left(1 + {\rm i}s\right)$ ?.

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