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 I need somebody to help me clarifiy the elementary knowledge for tetration Ember Edison Junior Fellow Posts: 38 Threads: 5 Joined: May 2019 07/01/2019, 12:11 PM (This post was last modified: 07/11/2019, 01:37 PM by Ember Edison.) I have been reading post in forum for two weeks. Now I feel I was too young, too simple, and naive for tetration. I need somebody to help me clarifiy the elementary knowledge for tetration. My understanding of the tetration is: Quote:Code definition: $\infty^*$=ComplexInfinity (infinite magnitude, undetermined complex phase) Not consider the branch cut: $tet_b(slog_b(z))=z$ $slog_b(tet_b(z))=z$ $tet_{sroot_h(z)}(h)=z$ and: $tet_{conj(b)}(conj(z))=tet_b(z)$ $slog_{conj(b)}(conj(z))=slog_b(z)$ $sroot_h(conj(z))=sroot_h(z)$ and: $tet_0(0)=1, tet_0(1)=0, tet_0(\infty^*)$is oscillates  infinitely, but maybe 0 and 1 are different branch of the infinite iterated exponential. $tet_1(0)=1, tet_1(1)=1, tet_1(\infty^*)=1$ in other bases: $tet_b(\infty^*)=\frac{\mathrm{W_{cut}}(-\ln{z})}{-\ln{z}},cut\in\mathbb{Z}$ $sroot_{\infty^*}(z)=({\frac{1}{z}})^{-\frac{1}{z}}$ tetration, super-root and super-logarithm is infinitely differentiable. (but I wasn't find code take the derivative...) If the bases is hyperbolic, there is only one "regular" super-function. If the bases is parabolic, will have at least 2 "regular" super-function.(Leau-Fatou-flower) The branch cut for super-function is infinitely. fatou.gp will use all "regular" super-function to refactoring tetration. bases regions for tetration: $base=\pm\infty$, Andrew Robbins base=0, not supported $base\in(0,e^{-e})$, unknown $base\in[e^{-e},1)$, Koenig, no code base=1, Andrew Robbins $base\in(1,e^{e^{-1}})$, Koenig, fatou.gp $base=e^{e^{-1}}$, Ecalle, fatou.gp $Arg(base)\in({\frac{14\pi}{30}},{\frac{21\pi}{30}})\wedge({\frac{42\pi}{30}},{\frac{47\pi}{30}}),\left| base \right|<1.76.$ill-region for Fatou. other, Fatou, fatou.gp « Next Oldest | Next Newest »

 Messages In This Thread I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 07/01/2019, 12:11 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by bo198214 - 07/09/2019, 09:26 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 07/11/2019, 03:10 AM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by sheldonison - 07/11/2019, 04:57 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 07/13/2019, 06:36 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by bo198214 - 07/11/2019, 08:16 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 07/13/2019, 06:49 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by sheldonison - 07/13/2019, 09:06 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by bo198214 - 07/15/2019, 11:21 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by bo198214 - 07/16/2019, 08:44 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 07/16/2019, 08:57 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 08/05/2019, 04:54 AM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by bo198214 - 08/13/2019, 08:32 PM RE: I need somebody to help me clarifiy the elementary knowledge for tetration - by Ember Edison - 08/26/2019, 01:44 PM

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