Solving tetration for base 0 < b

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Solving tetration for base 0 < b < e^-e

bo198214 Offline

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#22

09/17/2009, 08:01 AM (This post was last modified: 09/17/2009, 08:02 AM by bo198214.)

(09/14/2009, 09:43 PM)mike3 Wrote: Is there any way in which this could be done with something other than the matrix operator? For example, could a limit formula be used like that for \( b = e^{1/e} \), for this base (\( b = e^{-e} \)) even if convergence is dog slow?

Hm actually, I am not aware of such a limit formula. I only know \( |\lambda|\neq 0,1 \) and \( \lambda=1 \) but there should be also a formula somewhere for your case of \( \lambda=-1 \) (or generally for \( \lambda^m = 1 \) for some \( m \), here \( m=2 \)). If I have some time I will look through some books.

The powerseries development of the regular slog/sexp probably anyway has zero convergence radius.

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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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