Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*...
#3
(03/12/2013, 10:01 AM)Balarka Sen Wrote: Hi Mr. Helms,

If we consider the solution to the infinite product exp(x) = M * x * f(x) * f^[2](x) *..., it has the same solution as the one we get for M = 1 because of the fraction appears in your calculation which makes M/M = 1. So, it's likely that a factor appears but it seems your calculation doesn't counts it. It seems more like the constant of integration but except that it isn't integration - not very useful, but just my 2 cents.

Balarka
.
Hi Balarka -

yes, that seems also to me the reason. But why is that factor just exp(1)? In the discussion in MSE I've tried to give an answer to this, but that what I got is merely an intuition yet, not yet a usable formalism.

I've one time also looked at the gamma-function in terms of functional iteration and arrived at the "incomplete gamma" where a seemingly similar effect appears. It might be interesting to compare this.(If you're interested, here's the link: http://go.helms-net.de/math/musings/Unco...gGamma.pdf , see specifically at pg 12)

What I'm after with this is to see, how iterates of exp(x) might look expressed with that function f(x). (or whether it might be more sensical to discuss iterates of exp(x-1) in this context... )

Gottfried
Gottfried Helms, Kassel
Reply


Messages In This Thread
RE: Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... - by Gottfried - 03/12/2013, 10:13 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  New mathematical object - hyperanalytic function arybnikov 4 1,044 01/02/2020, 01:38 AM
Last Post: arybnikov
  Is there a function space for tetration? Chenjesu 0 662 06/23/2019, 08:24 PM
Last Post: Chenjesu
  Degamma function Xorter 0 1,123 10/22/2018, 11:29 AM
Last Post: Xorter
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,428 03/20/2018, 12:16 AM
Last Post: tommy1729
  THE problem with dynamics tommy1729 1 2,638 04/04/2017, 10:52 PM
Last Post: tommy1729
  Between addition and product ( pic ) tommy1729 4 4,120 07/10/2016, 07:32 AM
Last Post: Gottfried
  Should tetration be a multivalued function? marraco 17 18,624 01/14/2016, 04:24 AM
Last Post: marraco
  Introducing new special function : Lambert_t(z,r) tommy1729 2 4,004 01/10/2016, 06:14 PM
Last Post: tommy1729
  [sci.math] halting problem skeptic. tommy1729 0 1,851 05/30/2015, 09:24 PM
Last Post: tommy1729
Sad Tommy-Mandelbrot function tommy1729 0 2,181 04/21/2015, 01:02 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)