what is i factorial?

What is the factorial of i? Yes, the imaginary unit i. Does i factorial actually work? Yes, we will have to use the extension of factorial, namely the Pi function or the Gamma function. And we will also have to know how to deal with (a real number)^(complex exponent).

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[BobbyJCFHvLichtenstein]

sure math is magic, but the way he switches markers is another level

[tmfan]

*MINDBLOWN: i! rotated 180deg is still i!*

[ScottMaday]

Me: you know how many ways I can arrange √(-1) quarters?
Friend: what?
Me: You can arrange it 0.498015... - 0.1549498... _i_ ways
Friend: *what?*
Me: what?

[papsanlysenko]

It’s so sad when you can’t express an integral in the exact form(

[samharper]

Non-closed-form answers are so unsatisfying. :(

[fantiscious]

Here's a really cool fact: The *absolute value* of i factorial (aka its distance away from 0 on the complex plane) is actually √( π/sinh(π) ). That's crazy

[alextaunton]

I always find it funny how such things as i! or i^i or the antiderivative of x^i are not particularly special numbers. In fact, they almost seem arbitrary, given how fundamental i is to math. Honestly complex numbers fascinate me and I'm irritated at myself that I didn't truly appreciate their beauty until relatively recently.

[synaestheziac]

1:40 the “for you guys” here really gets me good

[antoniomodugno]

Can you do the derivate of n! and explain the digamma function

[swizzbeats]

Loved the video! And honestly one of my favourite channels on YouTube.

[coda-nu]

Can you prove that the real and imaginary parts of i! are irrational? Ive asked this to quora but nobody answered me

[Antipixl]

Can you do W(i) (Lambert W of i)? It also gives a cool complex number.
#yay from Costa Rica :D

[jangjerdum]

Real fans watched the unlisted version first

[MrCigarro]

Great video. At first sight I could not image how to go through this, the use of the Gamma function is brilliant. Thank you.

[TheReactor]

Your presentation is better than I have seen by others. However or in addition every time you say “fomula” I can’t help myself smiling.

[igxniisan]

3:22, when he says "lemme take that to the front" but what he actually does is taking that behind the integral.

[ehteshamashraf]

If you take the magnitude of the complex number i! (√(a^2+b^2)), it gives
π*cosech(π)!!😊

[EMorgensztern]

can you prove the integral formula for subfactorial please ?
#yay from France

[UltimateBargains]

I watched the entire video.
I only have one question.


What?

[quak]

as someone who has not learned any calc yet, but has learned polars, this really reminds me of rcistheta