HELP NEEDED: Exponential Factorial and Tetrations

[rsgerard]

Well what you are saying is not really the exponential factorial.

Correct.

5^4^3^2^1 = 5^(4^(3^(2^1))) = \( 5^{4^{3^{2^1}}} \ne 5^{(4\cdot 3 \cdot 2 \cdot 1)} \) = (((5^4)^3)^2)^1.

I think the problem here is that ttmath.org evaluates (a^b^c) incorrectly. It should use right-associative (^), but it seems to use left-associative (^), which is wrong.

Thanks for pointing out that this site is using left-association to evaluate. I guess I'm still curious to see if this constant really applies to these functions. I'll do a little more research myself. Thanks so much everyone.