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 Superroots and a generalization for the Lambert-W andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/21/2015, 05:05 AM I agree that it is a long-researched problem; trying to find a closed form for super-roots, or anything for that matter. Using a combination of known facts from the Tetration Ref I collected, I was able to find a simpler expression for the logarithmic power series expansion of $y = x^{x^x}$ than I remember from before. I think the ideal solution would be to find a recurrence equation similar to the one we know for n-th tetrates. I've attached a short discussion of the things we know that might help in finding a closed form. Attached Files   2015-11_SuperRoot3.pdf (Size: 123.09 KB / Downloads: 231) « Next Oldest | Next Newest »

 Messages In This Thread Superroots and a generalization for the Lambert-W - by Gottfried - 11/09/2015, 01:17 PM RE: Superroots and a generalization for the Lambert-W - by nuninho1980 - 11/09/2015, 11:27 PM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 11/10/2015, 12:06 PM RE: Superroots and a generalization for the Lambert-W - by tommy1729 - 11/10/2015, 09:38 AM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 11/10/2015, 12:04 PM RE: Superroots and a generalization for the Lambert-W - by tommy1729 - 11/10/2015, 11:19 PM RE: Superroots and a generalization for the Lambert-W - by andydude - 11/13/2015, 05:58 PM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 11/13/2015, 07:05 PM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 11/16/2015, 01:08 AM RE: Superroots and a generalization for the Lambert-W - by andydude - 11/21/2015, 05:05 AM RE: Superroots and a generalization for the Lambert-W - by andydude - 11/22/2015, 08:12 PM RE: Superroots and a generalization for the Lambert-W - by andydude - 11/24/2015, 12:51 AM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 11/24/2015, 02:56 AM RE: Superroots and a generalization for the Lambert-W - by andydude - 11/24/2015, 07:16 AM RE: Superroots and a generalization for the Lambert-W - by andydude - 11/24/2015, 07:00 AM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 12/01/2015, 03:13 PM RE: Superroots and a generalization for the Lambert-W - by tommy1729 - 12/01/2015, 11:58 PM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 12/02/2015, 03:49 AM RE: Superroots and a generalization for the Lambert-W - by tommy1729 - 12/02/2015, 01:22 PM RE: Superroots and a generalization for the Lambert-W - by andydude - 12/02/2015, 12:48 AM RE: Superroots and a generalization for the Lambert-W - by Gottfried - 12/02/2015, 02:43 AM RE: Superroots and a generalization for the Lambert-W - by andydude - 12/09/2015, 06:34 AM RE: Superroots and a generalization for the Lambert-W - by andydude - 12/30/2015, 09:49 AM

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