Continuous Hyper Bouncing Factorial

[Leo.W]

Yes, that's the bouncing Factorial. Thanks for doing the work I was too lazy to do, lol.

But the bouncing HYPER factorial. Get outta here, that's next century's problem, lmao.

I think it's easy to do so if we already find an asymptotic term? If we can prove that this hyper bouncing factorial growing fast almost as \(O(_xx)=O(x[6]2)\) and then recurrent!