Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[stuck] On the functional equation of the slog : slog(e^z) = slog(z)+1
#1
On the functional equation of the slog : slog(e^z) = slog(z)+1.

Related : http://math.eretrandre.org/tetrationforu...850&page=2

( post 15 mainly )

The issue is here that the functional equation cannot hold everywhere , see also the secondary fixpoints for example ( the related link above ).

Also we want to avoid singularities.

SO ultimately (imho) 2 questions :

1) when is a region A analytic ?
2) when does the functional equation hold ?

And the point of this thread is mainly that the 2 question are related !

The key is the n th derivative :

slog(exp(z)) = slog(z) + 1

DERIVATE

slog'(exp(z)) exp(z) = slog'(z)

2nd derivative

slog''(exp(z)) exp(z) + slog'(exp(z)) = slog''(z)

[stuck]

Sorry but this idea is a bit stuck. Its complicated.
I will update when possible. Feel free to comment.

regards

tommy1729
Reply
#2
Big question : what functional equations for slog(z) do we have in the branches near to the fundamental ??

regards

tommy1729
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
Big Grin Logical tetration equation Xorter 0 1,096 02/01/2018, 10:29 PM
Last Post: Xorter
  Functional power Xorter 0 1,125 03/11/2017, 10:22 AM
Last Post: Xorter
  Some sort equation ... tommy1729 0 1,388 10/15/2015, 12:12 PM
Last Post: tommy1729
  Some slog stuff tommy1729 15 10,838 05/14/2015, 09:25 PM
Last Post: tommy1729
  An intresting equation ? Taking squares by equation. tommy1729 0 1,484 05/08/2015, 11:37 PM
Last Post: tommy1729
  Conservation of functional equation ? tommy1729 0 1,525 05/01/2015, 10:03 PM
Last Post: tommy1729
  Is this THE equation for parabolic fix ? tommy1729 5 5,529 04/16/2015, 10:01 PM
Last Post: tommy1729
  Mick's differential equation tommy1729 3 2,933 04/10/2015, 04:14 PM
Last Post: tommy1729
  tommy equation tommy1729 3 3,570 03/18/2015, 08:52 AM
Last Post: sheldonison
  A limit exercise with Ei and slog. tommy1729 0 1,766 09/09/2014, 08:00 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)