Is there any meaning on $\displaystyle\Gamma(i)$

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Is there any meaning on the $\displaystyle\Gamma(i)$ ?

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Yes, its approximate value is $-0.15494982830181068512 -0.49801566811835604271i$.

The $\Gamma$-function is holomorphic on the whole complex plane, except for simple poles at $0$ and the negative integers.