Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
A Notation Question (raising the highest value in pow-tower to a different power)
#1
Dear users of the Tetration Forum, I am a new member and I have a question on notation for a function I have been trying to investigate.  I would like to denote a function using tetration notation, where the iteration index is integral and the highest tetrand (proper use?) is exponentiated to a different real value -(r) for positive real r.  I have been denoting it with the following, but am sure that this notation doesn't exactly mean what I want, I am hoping that someone may have a proper analytic formula to represent this function.  


Code:
[tex] $$f(x \vert k, r) = (x \uparrow \uparrow k)^{\uparrow(-r)} = x^{x^{x^{\rddots{x^{-r}}}}}$$ [\tex]

where the \rddots is defined (in preamble) as: \def\rddots#1{\cdot^{\cdot^{\cdot^{#1}}}}

This function has some interesting properties I would like to explore, but I want to make sure that I am using consistent notation, I hope that I have made clear what I mean by this, if I have not please feel free to message me privately, or respond to the thread in general. Thankyou very much for your time and consideration. 

PS - I apologize if I am breaking a forum rule by posting this in any way (I hope you will show mercy as I am new).  I am hoping to discover some of the properties of the above function and may have too hastily posted, please forgive my rudeness, ignorance of notation, and informality for posting LaTeX code in this way as I am not sure how to properly format my latex expressions, I tried including an image, but it seems as though you may only embed images through links, I may look at hosting images of LaTeX formatted equations in future posts via image sharing cites like imgur etc... (is this how it is done here?) I have also included a png of the formula.


Attached Files Image(s)
   
Reply


Messages In This Thread
A Notation Question (raising the highest value in pow-tower to a different power) - by Micah - 02/17/2019, 11:29 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Could there be an "arctic geometry" by raising the rank of all operations? Syzithryx 2 415 07/24/2019, 05:59 PM
Last Post: Syzithryx
  Math overflow question on fractional exponential iterations sheldonison 4 3,218 04/01/2018, 03:09 AM
Last Post: JmsNxn
  Functional power Xorter 0 1,193 03/11/2017, 10:22 AM
Last Post: Xorter
  2 fixpoints related by power ? tommy1729 0 1,324 12/07/2016, 01:29 PM
Last Post: tommy1729
  Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 1,457 09/06/2016, 04:23 PM
Last Post: tommy1729
  Inverse power tower functions tommy1729 0 1,757 01/04/2016, 12:03 PM
Last Post: tommy1729
  [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 11,229 12/28/2014, 10:22 PM
Last Post: MphLee
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 4,858 05/06/2014, 09:47 PM
Last Post: tommy1729
  about power towers and base change tommy1729 7 7,654 05/04/2014, 08:30 AM
Last Post: tommy1729
  Another question! JmsNxn 4 3,964 08/27/2013, 06:57 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)