Constructing the "analytical" formula for tetration.

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Constructing the "analytical" formula for tetration.

mike3 $Offline$
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Posts: 368
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Joined: Sep 2009

01/28/2011, 03:12 AM (This post was last modified: 01/28/2011, 03:13 AM by mike3.)

News: I may have just found a really complicated but "explicit" or "non-recursive" formula for the solutions of a general recurrence sequence of the form

$a_1 = r_{1, 1}$ ,
$a_n = \sum_{m=1}^{n-1} r_{n, m} a_m$

which these Schroder function coefficient equations belong to.

It's not "nice", though, but it looks to work (no proof yet as it was found by pattern examination). If you want details, just ask. But at least it seems to show that an explicit formula exists, so that there may perhaps be a simpler, more "elegant" one.

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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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