OK. I've seen threads about how to calculate $i!$, so I looked it up and it is approximately $0.49801566811835604271369111746219809195296296758765009289 - 0.15494982830181068512495513048388660519587965207932493026 i$.
The magnitude of $i!$ (I had to do some digging for this one) turns out to be $\sqrt{\frac{\pi}{\sinh\pi}}$.
But my question is, what are the closed-form expressions for those real and imaginary parts of $i!$? How would you write the $0.498015668...$ and $0.154949828...$ in terms of known mathematical constants? Is there even a way to do this?
I am using the Gamma function to generalize the factorial. So $i!=\Gamma\left(1+i\right)$.