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Question

Using the definition $$ \text{sf}(x) = \prod_{n=1}^{x} n! $$ Where would the Superfactorial ($\text{sf}(x)$) sit on the fast-growing hiearchy?

Context

The reason I am asking is because recently I have been pondering, which is faster growing, the hyperfactorial ($f_2(f_2(x))$ on the fast growing hiearchy), the exponential factorial ($f_3(x)$ on the fast-growing hiearchy) or the superfactorial?

Math Attack
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SebbyIsSwag
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1 Answers1

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According to Googology (see Section: Sloane and Plouffe), the given definition of superfactorial has a growth rate of about $f_2(n)$, which is $f_{1}^n(n)=n \cdot 2^n$ (see Definition of fast growing functions).

Marco Ripà
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