Constructing the "analytical" formula for tetration.
#13
(02/10/2011, 04:20 AM)mike3 Wrote: ....
Letting \( r_{n, m} = \frac{u^{n-1}}{1 - u^{n-1}} \frac{m!}{n!} \left{{n \atop m}\right} \), we now have \( \chi_n = a_n \), thus an explicit, non-recursive formula for the coefficients of the regular Schroder function of the decremented exponential.
What is the decremented exponential? I'm guessing here, (I apologize for sometimes having trouble seeing the big picture behind the equations), but are these coefficients related to the superfunction of f(z)=exp(z)-1?
-Sheldon
Reply


Messages In This Thread
RE: Constructing the "analytical" formula for tetration. - by sheldonison - 02/10/2011, 05:59 AM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Divergent Series and Analytical Continuation (LONG post) Caleb 54 57,140 03/18/2023, 04:05 AM
Last Post: JmsNxn
  Pictures of some generalized analytical continuations Caleb 18 18,782 03/17/2023, 12:56 AM
Last Post: tommy1729
  f(x+y) g(f(x)f(y)) = f(x) + f(y) addition formula ? tommy1729 1 3,113 01/13/2023, 08:45 PM
Last Post: tommy1729
  Constructing a real valued Fibonacci iteration--its relation to \(1/1+z\) JmsNxn 7 9,504 08/13/2022, 12:05 AM
Last Post: JmsNxn
  Constructing Tetration as a flip on its head JmsNxn 0 1,914 07/14/2022, 12:30 AM
Last Post: JmsNxn
  Constructing an analytic repelling Abel function JmsNxn 0 3,082 07/11/2022, 10:30 PM
Last Post: JmsNxn
Question Formula for the Taylor Series for Tetration Catullus 8 13,686 06/12/2022, 07:32 AM
Last Post: JmsNxn
  There is a non recursive formula for T(x,k)? marraco 5 11,852 12/26/2020, 11:05 AM
Last Post: Gottfried
  Constructing real tetration solutions Daniel 4 13,456 12/24/2019, 12:10 AM
Last Post: sheldonison
  Extrapolated FaĆ” Di Bruno's Formula Xorter 1 7,858 11/19/2016, 02:37 PM
Last Post: Xorter



Users browsing this thread: 1 Guest(s)