ArcFactorial / Inverse factorial

[tolik518]

Arc-Factorial or ArcFactorial or Arcfactorial or Inverse factorial is the inverse of a factorial: https://mizugadro.mydns.jp/t/index.php/ArcFactorial also see https://www.quora.com/Is-there-an-inverse-operation-for-factorials-like-division-is-the-inverse-of-multiplication

There's no standardized notation as far as I see, but possible notations would include: Arcfactorial(n), ¡n, n¡, n!^-1

[Aras14HD]

Because n! = gamma(n+1) n = agamma(y)-1, so we can use this: https://en.wikipedia.org/wiki/Inverse_gamma_function

Might have more resources for approximations.

[Aras14HD]

I feel that ¡n seems most like an arc-factorial, n¡ seems more like an arc-sub-factorial to me. (Basing of spanish ¡...!)

Using that, ¡n! would be factorial of arc-factorial (or vice versa) of n (is n). (sub-factorial equivalent !n¡)

Arc-sub-factorials (and maybe arc(-multi)-termials like ¿n?) would be a separate issue though, if they are doable (arc-termial should be easy, but arc-sub-factorials and any multi versions might be harder).

[tolik518]

I feel that ¡n seems most like an arc-factorial, n¡ seems more like an arc-sub-factorial to me. (Basing of spanish ¡...!)

¡n looks for me more like an arc-subfactorial since its just an upside down exclamation-mark on the same place as it would be for an subfactorial. On the other hand I really like your idea of the spanish ¡...! and I'm more inclined to agree with you

Edit: the more I think about it, the more I like the idea of establishing ¡...!

[Aras14HD]

Arc multifactorials don't seem very possible to me. Arc-termials however are simple (just solving a quadratic)

$$¿n = \frac{1}{2} + \sqrt{\frac{1}{4}+n}$$