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Question Number 163548 by HongKing last updated on 07/Jan/22

$$\mathrm{Lambert}\mathrm{series}\mathrm{type}\mathrm{representation}$$$$\mathrm{for}\sqrt{-1}\mathrm{factorial}$$$$\left({\mathrm{i}}^{\mathbf{i}}\right)!(-{\mathrm{i}}^{\mathbf{i}})!=1-2\underset{\mathbf{n}=1}{\sum ^{\mathrm{\infty }}}\frac{{(-1)}^{\mathbf{n}}}{{\mathrm{e}}^{\mathit{\pi }}{\mathrm{n}}^2-1}$$

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