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 Solving tetration for base 0 < b < e^-e mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 09/13/2009, 09:49 AM (This post was last modified: 09/13/2009, 09:51 AM by mike3.) Why not use the entire? Because the behavior is not consistent. It seems stranger to imagine a function that has singularities for only real bases $b \geq e^{-e}$, then suddenly it becomes free of them and entire for all $b < e^{-e}$. It's two wildly different analytical behaviors and that doesn't make much sense. Ideally it would be nice to be able to interpret the tetration at $0 < b < e^{-e}$ to be what you'd get if you did an analytical continuation in the base from $b > e^{-e}$ through the complex plane. Finally, at the integer towers of this base, we are still dealing with real numbers: when we take the log of $^0 b = 1$ for $0 < b < e^{-e}$ to get $^{-1} b$ as 0, we are still using a real logarithm of a real number to a real base. So why not continue using this principal real logarithm for the rest of the tet function at this base? « Next Oldest | Next Newest »

 Messages In This Thread Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 02:00 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 06:56 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:20 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 07:40 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:47 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:07 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 08:35 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:50 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 03:48 PM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 09:04 PM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 06:14 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 07:24 AM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 09:57 AM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 11:23 AM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 11:44 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/14/2009, 09:43 PM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/17/2009, 08:01 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/17/2009, 11:03 AM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 01:34 PM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 07:34 PM RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/14/2009, 02:02 PM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 08:08 AM RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 09:49 AM RE: Solving tetration for base 0 < b < e^-e - by tommy1729 - 09/18/2009, 12:16 PM RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/18/2009, 01:00 PM

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