Thread Rating:
  • 1 Vote(s) - 1 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tetration extension for bases between 1 and eta
#13
Sorry for continuing to post more limit formulas but I found another that I do not think has been mentioned before.



which is the same as




This works whenever a function has a regular attracting or repelling fixed point that it increases through. For it to work near a repelling fixed point you simply let k approach negative infinity.

Also note that gives a fairly decent aproximation of near a fixed point

Some pictures.
Red is blue is and green is

sin[x]
   

e^x-1, x<0
   


thanks.
Reply


Messages In This Thread
RE: Tetration extension for bases between 1 and eta - by dantheman163 - 12/17/2009, 02:40 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Possible continuous extension of tetration to the reals Dasedes 0 1,210 10/10/2016, 04:57 AM
Last Post: Dasedes
  Andrew Robbins' Tetration Extension bo198214 32 40,886 08/22/2016, 04:19 PM
Last Post: Gottfried
  Why bases 0<a<1 don't get love on the forum? marraco 20 15,824 04/19/2015, 05:53 PM
Last Post: Gottfried
  Bundle equations for bases > 2 tommy1729 0 1,668 04/18/2015, 12:24 PM
Last Post: tommy1729
  on constructing hyper operations for bases > eta JmsNxn 1 2,522 04/08/2015, 09:18 PM
Last Post: marraco
  Non-trivial extension of max(n,1)-1 to the reals and its iteration. MphLee 3 3,634 05/17/2014, 07:10 PM
Last Post: MphLee
  extension of the Ackermann function to operators less than addition JmsNxn 2 3,840 11/06/2011, 08:06 PM
Last Post: JmsNxn
  Alternate solution of tetration for "convergent" bases discovered mike3 12 17,272 09/15/2010, 02:18 AM
Last Post: mike3
  my accepted bases tommy1729 0 2,094 08/29/2010, 07:38 PM
Last Post: tommy1729
  [Regular tetration] bases arbitrarily near eta Gottfried 0 2,733 08/22/2010, 09:01 AM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)