Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Generalized arithmetic operator
#13
Quote:what lies between tetration and pentation ?
Do we know what lies between addition and multiplication, or multiplication and exponentiation? I would be happy to know those first. I assume they would be simpler to find, but I can also imagine that they would be equally difficult to find.

Quote:Question : if we say S^[a+b](f(x)) = S^[a](S^[b](f(x)) = S^[b](S^[a](f(x))
Then what is S^[1/2](f(x)) ? Or what is S^[1/2](exp(x)) ?
I found an answer to part of your question. By that I mean I was able to find S^[1/2](exp(x)):

By definition:


So we are trying to find some function such that


If we define such that


then






, where W is the Lambert W function





There is your half-superfunction of exp(x).
Reply


Messages In This Thread
Generalized arithmetic operator - by hixidom - 03/11/2014, 03:52 AM
RE: Generalized arithmetic operator - by JmsNxn - 03/11/2014, 03:15 PM
RE: Generalized arithmetic operator - by hixidom - 03/11/2014, 06:24 PM
RE: Generalized arithmetic operator - by MphLee - 03/11/2014, 10:49 PM
RE: Generalized arithmetic operator - by hixidom - 03/11/2014, 11:20 PM
RE: Generalized arithmetic operator - by MphLee - 03/12/2014, 11:18 AM
RE: Generalized arithmetic operator - by JmsNxn - 03/12/2014, 02:59 AM
RE: Generalized arithmetic operator - by hixidom - 03/12/2014, 04:37 AM
RE: Generalized arithmetic operator - by MphLee - 03/12/2014, 06:19 PM
RE: Generalized arithmetic operator - by hixidom - 03/12/2014, 06:43 PM
RE: Generalized arithmetic operator - by hixidom - 03/22/2014, 12:06 AM
RE: Generalized arithmetic operator - by hixidom - 03/22/2014, 12:42 AM
RE: Generalized arithmetic operator - by hixidom - 06/11/2014, 05:10 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,076 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Tetration and Sign operator tetration101 0 209 05/15/2019, 07:55 PM
Last Post: tetration101
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 569 03/03/2019, 08:55 AM
Last Post: Chenjesu
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 15,124 08/22/2016, 12:19 AM
Last Post: JmsNxn
  [rule 30] Is it possible to easily rewrite rule 30 in terms of modular arithmetic ? tommy1729 0 1,429 07/24/2014, 11:09 PM
Last Post: tommy1729
  Tetration and modular arithmetic. tommy1729 0 1,794 01/12/2014, 05:07 AM
Last Post: tommy1729
  Hyper operator space JmsNxn 0 1,729 08/12/2013, 10:17 PM
Last Post: JmsNxn
  Generalized Bieberbach conjectures ? tommy1729 0 1,558 08/12/2013, 08:11 PM
Last Post: tommy1729
  Operator definition discrepancy? cacolijn 2 3,536 01/07/2013, 09:13 AM
Last Post: cacolijn
  Generalized Wiener Ikehara for exp[1/2](n) instead of n ? tommy1729 0 1,582 12/17/2012, 05:01 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)