Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Should tetration be a multivalued function?
#14
Hold on we can do a bit better.

For base sqrt(2) = a using sheldon's y and z.

a^^0 is defined by

a^^0 ^ a^^0 = 2^4 = 4^2 = 16.
( 2 and 4 are a^^oo or the fixpoints )

So a^^0 = ssqrt(16).

From sheldon we then get

a^(y z) = 16.

subst a = sqrt(2) [ for example , this idea works for other bases too ]

=> y z = 8.

Now notice r = -(r+1) for r = -1/2.

So a^^(-1/2) ^ 2 = 8.

So a^^(-1/2) = sqrt( 8 ) = 2 sqrt(2).

Since we have a^^0 and a^^(-1/2) we actually have

a^^(K/2) for all integer K.

Maybe this idea can be extended to a unique analytic solution ...

¯\_(ツ)_/¯

Regards

tommy1729
The master
Reply


Messages In This Thread
RE: Should tetration be a multivalued function? - by tommy1729 - 01/10/2016, 03:37 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 385 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 501 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 952 10/22/2018, 11:29 AM
Last Post: Xorter
  Introducing new special function : Lambert_t(z,r) tommy1729 2 3,731 01/10/2016, 06:14 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 2,019 04/21/2015, 01:02 PM
Last Post: tommy1729
  The inverse gamma function. tommy1729 3 7,753 05/13/2014, 02:18 PM
Last Post: JmsNxn
  entire function close to sexp ?? tommy1729 8 9,732 04/30/2014, 03:49 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 7,053 07/17/2013, 09:46 AM
Last Post: Gottfried
  Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 3,104 06/15/2013, 08:02 PM
Last Post: MphLee
  Hyperzeta function Balarka Sen 7 8,158 05/08/2013, 01:36 PM
Last Post: Balarka Sen



Users browsing this thread: 1 Guest(s)