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 base holomorphic tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 11/05/2009, 02:12 PM Hey folks, until now we mainly considered holomorphy in the second argument $t$ of tetration: $b [4] t = {\exp_b}^{\circ t}(1)$. If we now fix $t$ and demand also the function $f_t(b)=b [4] t$ to be analytic on one small interval $b\in(b_1,b_2)$, the function $f_t$ is already determined for all other bases, particularly for bases $b>e^{1/e}$ by analytic continuation along the real axis (if there is no singularity at $b=e^{1/e}$). For bases $1 we know that the regular iteration at the lower fixed point is analytic there and continuable to 1. So the question would be to what values the regular iteration $f_t$ continues for $b>e^{1/e}$. I guess it has a branch point at $b^{1/b}$ and continues to complex values beyond $e^{1/e}$. I will explore this thought more concretely in the following posts. « Next Oldest | Next Newest »

 Messages In This Thread base holomorphic tetration - by bo198214 - 11/05/2009, 02:12 PM RE: base holomorphic tetration - by Base-Acid Tetration - 11/05/2009, 10:50 PM RE: base holomorphic tetration - by mike3 - 11/06/2009, 04:15 AM RE: base holomorphic tetration - by mike3 - 11/06/2009, 11:58 AM RE: base holomorphic tetration - by bo198214 - 11/06/2009, 12:12 PM RE: base holomorphic tetration - by mike3 - 11/06/2009, 09:16 PM RE: base holomorphic tetration - by bo198214 - 11/06/2009, 11:29 PM RE: base holomorphic tetration - by mike3 - 11/07/2009, 12:23 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 08:17 AM RE: base holomorphic tetration - by mike3 - 11/07/2009, 08:21 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 09:55 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 04:47 PM RE: base holomorphic tetration - by bo198214 - 11/08/2009, 05:39 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:27 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:25 PM RE: base holomorphic tetration - by bo198214 - 11/08/2009, 08:44 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 09:51 PM

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