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 question about regular iteration, also about tetration properties in general Base-Acid Tetration Fellow Posts: 94 Threads: 15 Joined: Apr 2009 05/05/2009, 03:27 AM (This post was last modified: 05/12/2009, 03:55 AM by Base-Acid Tetration.) So, Andysus bo198214, $\frac{d}{dx}\exp^{\circ x} (\pm W(-1)) = \exp'(\pm W(-1))^x = \exp(\pm W(-1))^x$? Where do you get from this to derive your tetration? Does $\lim_{y \to \infty} {}^{\pm iy} e = \mbox{fixed point of logarithm}= \pm W(-1)$, as in Kouznetsov's, in your tetration? Also, how does one get the differential equation $\ln (a)\frac{({}^{x+1} a)'}{({}^x a)'}={}^x a$? Edit: Oh, it comes from the definition of tetration. ${}^{x} a = a^{{}^{x-1} a}$ $[{}^{x} a]' = ({}^{x-1} a)' a^{{}^{x-1} a} \, \ln a$ $\frac{({}^{x} a)'}{ \ln{a} \, ({}^{x-1} a)' } = {}^x a, \, {}^0 a=1$ « Next Oldest | Next Newest »

 Messages In This Thread question about regular iteration, also about tetration properties in general - by Base-Acid Tetration - 05/03/2009, 02:49 AM RE: question about regular iteration - by bo198214 - 05/03/2009, 07:05 AM RE: question about regular iteration - by Base-Acid Tetration - 05/04/2009, 04:23 AM RE: question about regular iteration - by bo198214 - 05/04/2009, 07:34 AM RE: question about regular iteration - by Base-Acid Tetration - 05/05/2009, 03:27 AM RE: question about regular iteration - by bo198214 - 05/10/2009, 09:32 AM

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