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 Superroots and a generalization for the Lambert-W Gottfried Ultimate Fellow Posts: 765 Threads: 119 Joined: Aug 2007 11/10/2015, 12:04 PM (This post was last modified: 11/10/2015, 12:06 PM by Gottfried.) (11/10/2015, 09:38 AM)tommy1729 Wrote: Conjecture 3.1 fails because the left hand side has radius going to 0.Hmm, I've not yet settled everything about this in my mind. I've of course seen, that with increasing n the convergence-radius of the function $\;^n W$ decreases. However, as usually, if a function can be analytically continued (beyond its radius of convergence) for instance by Euler-summation, I assume, that the result is still meaningful. And we have here the possibility for Euler-summation, so I think there is a true analytic continuation. However, I don't know yet whether this can be correctly inserted in my conjecture-formula for the limit-case. Quote:It is a mystery how you intend to solve the cases x^^(3/2) = v though. As I understand this, this is using fractional iteration heights. As I described my exercises, I'm concerned with the unknown bases, and am using integer heights so far, not fractional heights ( superroot, not superlog) Gottfried Gottfried Helms, Kassel « 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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