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 Constructing the "analytical" formula for tetration. Gottfried Ultimate Fellow Posts: 765 Threads: 119 Joined: Aug 2007 01/24/2011, 08:56 AM Mike - without having it definite, I think that your recursive description should be the same as that in the eingenvalue/eigensystem-computation in the APT-article: it is just a simple procedure and works fast. I was as well looking for a simpler, non-recursive description But I didn't find anything convincing. The only thing I found was that method which solves linear equation systems using the (u-1)(u^2-1)...() - denominators and assumes that at integer heights the numerator must be evenly divisible by that denominator plus the assumption, that the first and last row of the coefficients-matrices are the Stirlingnumbers first and second kind, respectively (or opposite). With this each coefficient-matrix can be determined separately, nonrecursive at least in the sense that the coefficients-matrices (and thus the computation of their second and their last columns) are independent of each other. (Don't know whether the description of this in the mentioned APT-article was too short/imprecise?) I didn't proceed there - it seemed to be too complicated and does not give an optimization over the efficient recursive procedure ; maybe you could find an improvement once the system of conditions is formally stated in terms of linear equations/matrix-formula and thus possibly get a more explicite expression in terms of the "curlybraces" ;-) only. Well, I'll give it another try myself today, but my emphasis on this has a bit cooled down, to be frank... Gottfried Gottfried Helms, Kassel « 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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