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 Constructing the "analytical" formula for tetration. mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 02/10/2011, 07:35 AM (This post was last modified: 02/10/2011, 07:38 AM by mike3.) (02/10/2011, 05:59 AM)sheldonison Wrote: (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 Earlier here, I mention finding the regular Schroder function of the function $e^{uz} - 1$, about the fixed point of $z = 0$ of course. That function is the decremented exponential. « Next Oldest | Next Newest »

 Messages In This Thread Constructing the "analytical" formula for tetration. - by mike3 - 01/17/2011, 01:05 PM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/17/2011, 10:10 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/22/2011, 04:00 AM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/24/2011, 08:56 AM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/28/2011, 03:12 AM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/28/2011, 02:49 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/28/2011, 09:12 PM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/28/2011, 10:42 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/29/2011, 12:10 AM RE: Constructing the "analytical" formula for tetration. - by mike3 - 02/10/2011, 04:20 AM RE: Constructing the "analytical" formula for tetration. - by sheldonison - 02/10/2011, 05:59 AM RE: Constructing the "analytical" formula for tetration. - by mike3 - 02/10/2011, 07:35 AM RE: Constructing the "analytical" formula for tetration. - by tommy1729 - 01/23/2011, 10:59 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/24/2011, 04:34 AM

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