Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tribonacci interpolation ?
#1
I was thinking about (real) interpolation of the tribonacci sequence.

Of course there is the real part of the binet like analogue.
But I do not want that solution or at least I want to arrive at it in a different way.

Instead of considering asymptotics , positive derivatives , fake function theory and the recent alike stuff , I was more intrested in using more "classical" stuff.

Considering that a recursion is close to an iteration I got the idea to use superfunctions.

---
I must note however that a continuum sum might also be usefull here !!
---


But then I encountered a problem.
It can probably be fixed though.

This is the idea I had and the trouble I encountered ;

trib(x) = trib(x-1) + trib(x-2) + trib(x-3)

Define rat(x) = trib(x+1)/trib(x).

Now

rat(x+1) = ( trib(x+1) + trib(x) + trib(x-1) ) / trib(x+1)

= 1 + (trib(x) + trib(x-1))/trib(x+1)

= 1 + 1/rat(x-1) + rat(x-2)/rat(x-1)

This looks familiar ...

Somos , Fibonacci ... hmm.

( still thinking , might edit )

---
Notice the analogue for Fibonacci works : we get

ratfibo(x) = 1 + 1/ratfibo(x) which has the golden mean and 1 - golden mean as its fixpoints.

Im trying to get the tribonacci constant as a fixpoint here ...
---

regards

tommy1729
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  [Update] Comparision of 5 methods of interpolation to continuous tetration Gottfried 30 27,074 02/04/2014, 12:31 AM
Last Post: Gottfried
  Self tetraroot constructed via Newton series interpolation mike3 2 6,261 07/11/2010, 03:38 AM
Last Post: mike3
  A false interpolation paradigm (?); a reconsideration Gottfried 4 6,915 09/17/2009, 08:17 AM
Last Post: bo198214
  exponential polynomial interpolation Gottfried 3 6,772 07/16/2008, 10:32 PM
Last Post: andydude
  A related discussion on interpolation: factorial and gamma-function Gottfried 6 9,907 06/27/2008, 06:38 PM
Last Post: Gottfried
  polynomial interpolation to fractional iteration Gottfried 3 7,895 12/23/2007, 03:40 PM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)