11/12/2009, 10:42 PM
I have been studying exponential factorials and have been looking for the equivalent tetration. For example:
5^4^3^2^1= 5.9 e16
10^9^8^7^6^5^4^3^2^1 = 10 e363879
I believe as n goes to infinity the exponential factorial can be written as a tetration:
n^(n-1)^(n-2)...^2^1 =
(n/alpha)^(n/alpha)^(n/alpha)^(n/alpha)...repeated n times
where alpha is Feigenbaum constant 2.5029...
I have been testing this on this site:
http://www.ttmath.org/online_calculator
It does seem very very close for up to 25^24^23^...^2^1 can be written as an equivalent tetration. I would anyones input to see if they can help me determine it can be written as a tetration more rigorously. Thanks very much
Ryan Gerard
5^4^3^2^1= 5.9 e16
10^9^8^7^6^5^4^3^2^1 = 10 e363879
I believe as n goes to infinity the exponential factorial can be written as a tetration:
n^(n-1)^(n-2)...^2^1 =
(n/alpha)^(n/alpha)^(n/alpha)^(n/alpha)...repeated n times
where alpha is Feigenbaum constant 2.5029...
I have been testing this on this site:
http://www.ttmath.org/online_calculator
It does seem very very close for up to 25^24^23^...^2^1 can be written as an equivalent tetration. I would anyones input to see if they can help me determine it can be written as a tetration more rigorously. Thanks very much
Ryan Gerard
