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 64,818 03/18/2023, 04:05 AM
Last Post: JmsNxn
  Pictures of some generalized analytical continuations Caleb 18 21,707 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 3,559 01/13/2023, 08:45 PM
Last Post: tommy1729
  Constructing a real valued Fibonacci iteration--its relation to \(1/1+z\) JmsNxn 7 10,765 08/13/2022, 12:05 AM
Last Post: JmsNxn
  Constructing Tetration as a flip on its head JmsNxn 0 2,132 07/14/2022, 12:30 AM
Last Post: JmsNxn
  Constructing an analytic repelling Abel function JmsNxn 0 3,362 07/11/2022, 10:30 PM
Last Post: JmsNxn
Question Formula for the Taylor Series for Tetration Catullus 8 15,029 06/12/2022, 07:32 AM
Last Post: JmsNxn
  There is a non recursive formula for T(x,k)? marraco 5 12,974 12/26/2020, 11:05 AM
Last Post: Gottfried
  Constructing real tetration solutions Daniel 4 14,149 12/24/2019, 12:10 AM
Last Post: sheldonison
  Extrapolated FaĆ” Di Bruno's Formula Xorter 1 8,245 11/19/2016, 02:37 PM
Last Post: Xorter



Users browsing this thread: 1 Guest(s)