A random question for mathematicians regarding i and the Fibonacci sequence.
What is the Fibonacci root of i, or to put it another way, what is the equation of x when       
 \( \Large \quad \quad      {({1+\sqrt 5\over 2})^x-(-1)^x ( { 2\over 1+\sqrt 5})^x \over \sqrt 5}=n \)  


All I need is a formular and I am capable of just entering the eqution and i straight into Google calculator to get a result.

I'm interested as decimal numbers entered into the Fibonacci function manly get complex results which shows a link between the function and i, and suggests that the Fibonacci root of i might not be complex and might be of some importance.

I know this isn't really to do with Tetration, but I've asked this across the internet and have not have any replies and I'll be greatfull for any help.

(08/07/2011, 11:17 PM)robo37 Wrote: What is the Fibonacci root of i, or to put it another way, what is the equation of x when ((1+sqrt 5)/2)^x-((-1)^x/((1+sqrt 5)/2)^x)))/sqrt 5=n?
You did not rationalize your denominator.
The numerical solutions to Fibonacci(x)=i are
x ~ -.42709179162288762 - .22105741463869769 * I
x ~ 1.67226840550786450 + 3.2642638352534426 * I.
I do not know of any closed forms for those numbers.
For an inverse to the Fibonacci function, there are no result found in terms of standard mathematical functions.
Please remember to stay hydrated.
ฅ(ミ⚈ ﻌ ⚈ミ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\

Possibly Related Threads…
Thread Author Replies Views Last Post
  Fibonacci as iteration of fractional linear function bo198214 48 3,431 09/14/2022, 08:05 AM
Last Post: Gottfried
  Constructing a real valued Fibonacci iteration--its relation to \(1/1+z\) JmsNxn 7 441 08/13/2022, 12:05 AM
Last Post: JmsNxn
  [question] Local to global and superfunctions MphLee 8 644 07/17/2022, 06:46 AM
Last Post: JmsNxn
  Question about tetration methods Daniel 17 1,322 06/22/2022, 11:27 PM
Last Post: tommy1729
  Interpolating an infinite sequence ? tommy1729 14 1,158 06/17/2022, 10:41 PM
Last Post: tommy1729
  A question concerning uniqueness JmsNxn 4 10,000 06/10/2022, 08:45 AM
Last Post: Catullus
  Math.Stackexchange.com question on extending tetration Daniel 3 2,379 03/31/2021, 12:28 AM
Last Post: JmsNxn
  Kneser method question tommy1729 9 12,794 02/11/2020, 01:26 AM
Last Post: sheldonison
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 13,244 02/18/2019, 10:34 PM
Last Post: Micah
  Math overflow question on fractional exponential iterations sheldonison 4 10,865 04/01/2018, 03:09 AM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)