• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 HELP NEEDED: Exponential Factorial and Tetrations rsgerard Junior Fellow Posts: 11 Threads: 5 Joined: May 2008 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 dantheman163 Junior Fellow Posts: 13 Threads: 3 Joined: Oct 2009 11/12/2009, 11:19 PM (11/12/2009, 10:42 PM)rsgerard Wrote: 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 Well what you are saying is not really the exponential factorial. What you wrote above is the same as $x^{(x-1)!}$ The value of $5^{4^{3^{2^1}}}$ is acutaly more like 6.206e+183230 As for (11/12/2009, 10:42 PM)rsgerard Wrote: n^(n-1)^(n-2)...^2^1 = (n/alpha)^(n/alpha)^(n/alpha)^(n/alpha)...repeated n times I would have to look into this more to see how close to $x^{(x-1)!}$ it is nuninho1980 Fellow Posts: 95 Threads: 6 Joined: Apr 2009 11/12/2009, 11:19 PM (This post was last modified: 11/12/2009, 11:21 PM by nuninho1980.) aah! it's normal. sorry. I removed. andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/12/2009, 11:46 PM Honestly, I have never heard of the Feigenbaum constant before. Is 2.5029 the value for exponential functions? or all functions? andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/12/2009, 11:51 PM (This post was last modified: 11/12/2009, 11:53 PM by andydude.) (11/12/2009, 11:19 PM)dantheman163 Wrote: 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. rsgerard Junior Fellow Posts: 11 Threads: 5 Joined: May 2008 11/13/2009, 02:27 AM (11/12/2009, 11:51 PM)andydude Wrote: (11/12/2009, 11:19 PM)dantheman163 Wrote: 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. « Next Oldest | Next Newest »

 Possibly Related Threads... Thread Author Replies Views Last Post Math overflow question on fractional exponential iterations sheldonison 4 3,724 04/01/2018, 03:09 AM Last Post: JmsNxn Are tetrations fixed points analytic? JmsNxn 2 2,968 12/14/2016, 08:50 PM Last Post: JmsNxn Theorem in fractional calculus needed for hyperoperators JmsNxn 5 6,582 07/07/2014, 06:47 PM Last Post: MphLee Crazy conjecture connecting the sqrt(e) and tetrations! rsgerard 7 12,442 03/27/2014, 11:20 PM Last Post: tommy1729 An exponential "times" table MikeSmith 0 1,825 01/31/2014, 08:05 PM Last Post: MikeSmith exponential baby Mandelbrots? sheldonison 0 2,044 05/08/2012, 06:59 PM Last Post: sheldonison exponential distributivity bo198214 4 6,542 09/22/2011, 03:27 PM Last Post: JmsNxn Base 'Enigma' iterative exponential, tetrational and pentational Cherrina_Pixie 4 9,739 07/02/2011, 07:13 AM Last Post: bo198214 Two exponential integrals Augustrush 2 4,395 11/10/2010, 06:44 PM Last Post: Augustrush Exponential factorial mike3 3 5,957 10/07/2009, 02:04 AM Last Post: andydude

Users browsing this thread: 1 Guest(s)