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 base holomorphic tetration bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 11/07/2009, 08:17 AM (11/07/2009, 12:23 AM)mike3 Wrote: By a "graph that shows the convergence of the series" you mean like a graph of partial sums? Yes, yes, x-axis: n, y-axis: n-th partial sum. Quote:Also, I could try a root test or ratio test but I think to make it really good I'll need more terms... With root test the same: x-axis: n, y-axis: $1/\sqrt[n]{|a_n|}$. The root-test should converge to something bigger than the distance from the development point to the perhaps-singularity. Quote:I just saw the paper and there appears to be a recurrence formula on page 8 but am a little confused by the notation. Specifically, what's ${g^m}_n$ supposed to be? nth Taylor coefficient of m iterations of g? But we have not yet determined g, so how can we iterate? In this draft integer-iteration is always denoted by $f^{[n]}$, while power is as usual $f^{n}$. ${g^m}_n$ depends only on values $g_k$, $k\le n$. You can take the polynomial of g truncated to n, then take the m-th power and then get the coefficient at n. « Next Oldest | Next Newest »

 Messages In This Thread base holomorphic tetration - by bo198214 - 11/05/2009, 02:12 PM RE: base holomorphic tetration - by Base-Acid Tetration - 11/05/2009, 10:50 PM RE: base holomorphic tetration - by mike3 - 11/06/2009, 04:15 AM RE: base holomorphic tetration - by mike3 - 11/06/2009, 11:58 AM RE: base holomorphic tetration - by bo198214 - 11/06/2009, 12:12 PM RE: base holomorphic tetration - by mike3 - 11/06/2009, 09:16 PM RE: base holomorphic tetration - by bo198214 - 11/06/2009, 11:29 PM RE: base holomorphic tetration - by mike3 - 11/07/2009, 12:23 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 08:17 AM RE: base holomorphic tetration - by mike3 - 11/07/2009, 08:21 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 09:55 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 04:47 PM RE: base holomorphic tetration - by bo198214 - 11/08/2009, 05:39 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:27 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:25 PM RE: base holomorphic tetration - by bo198214 - 11/08/2009, 08:44 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 09:51 PM

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