• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Kneser's Super Logarithm mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 01/28/2010, 08:52 PM (01/27/2010, 08:30 PM)sheldonison Wrote: (01/27/2010, 06:28 PM)mike3 Wrote: Ah. What do you mean by the Fourier series "exponentially decays to a constant as i increases"? Do you mean the coefficients of the series (in which case how could it converge?)? Do you mean the behavior toward imaginary infinity (if so, does it decay to the two principal fixed points of exp)?I mean the 1-cyclic repeating function $(\theta(z)-z)$ exponentially decays to a constant as $\Im(z)$ increases. After the Riemann mapping, it's individual Fourier series terms all decay to zero as imaginary increases. The terms grow as we approach the real axis, and at the real axis, it has singularities at integer values. The complex sexp developed from the fixed point (the inverse Abel function), $\psi^{-1}(z)$ already goes to the fixed point as $\Im(z)$ increases, and as $Re(z)$ decreases. It would be nice to have a graph of $\psi^{-1}(z)$, which becomes super-exponential (complex only) as $\Re(z)$ increases, and as $\Im(z)$ decreases, and goes to the fixed point as $\Im(z)$ increases, and as $\Re(z)$ decreases. Finally, $\operatorname{sexp}_e(z)=\psi^{-1}(\theta(z))$, so as as $\Im(z)$ increases, the sexp_e(z) will converge to $\psi^{-1}(z+k)$, where k is a small constant. - Shel So then it would seem to agree with the Kouznetsov function, then, wouldn't it, i.e. the $\operatorname{tet}_e(z)$ function developed this way decays to approximately $0.318 \pm 1.337i$ as $z \rightarrow \pm i \infty$? Hmm. Does this Kneser method work for other bases, too? Can it be used at a complex base, e.g. $2 + 1.5i$? « Next Oldest | Next Newest »

 Messages In This Thread Kneser's Super Logarithm - by bo198214 - 11/19/2008, 02:20 PM RE: Kneser's Super Logarithm - by bo198214 - 11/19/2008, 03:25 PM RE: Kneser's Super Logarithm - by sheldonison - 01/23/2010, 01:01 PM RE: Kneser's Super Logarithm - by mike3 - 01/25/2010, 06:35 AM RE: Kneser's Super Logarithm - by sheldonison - 01/25/2010, 07:42 AM RE: Kneser's Super Logarithm - by mike3 - 01/26/2010, 06:24 AM RE: Kneser's Super Logarithm - by sheldonison - 01/26/2010, 01:22 PM RE: Kneser's Super Logarithm - by mike3 - 01/27/2010, 06:28 PM RE: Kneser's Super Logarithm - by sheldonison - 01/27/2010, 08:30 PM RE: Kneser's Super Logarithm - by mike3 - 01/28/2010, 08:52 PM RE: Kneser's Super Logarithm - by sheldonison - 01/28/2010, 10:08 PM RE: Kneser's Super Logarithm - by mike3 - 01/29/2010, 06:43 AM RE: Kneser's Super Logarithm - by bo198214 - 01/26/2010, 11:19 PM RE: Kneser's Super Logarithm - by sheldonison - 01/27/2010, 07:51 PM RE: Kneser's Super Logarithm - by bo198214 - 11/22/2008, 06:11 PM RE: Kneser's Super Logarithm - by bo198214 - 11/23/2008, 01:00 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Kneser method question tommy1729 9 282 02/11/2020, 01:26 AM Last Post: sheldonison Is bugs or features for fatou.gp super-logarithm? Ember Edison 10 2,945 08/07/2019, 02:44 AM Last Post: Ember Edison A fundamental flaw of an operator who's super operator is addition JmsNxn 4 7,016 06/23/2019, 08:19 PM Last Post: Chenjesu Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 3,597 06/10/2019, 04:29 AM Last Post: Ember Edison Inverse super-composition Xorter 11 13,192 05/26/2018, 12:00 AM Last Post: Xorter The super 0th root and a new rule of tetration? Xorter 4 4,091 11/29/2017, 11:53 AM Last Post: Xorter Solving tetration using differintegrals and super-roots JmsNxn 0 1,960 08/22/2016, 10:07 PM Last Post: JmsNxn The super of exp(z)(z^2 + 1) + z. tommy1729 1 2,661 03/15/2016, 01:02 PM Last Post: tommy1729 Super-root 3 andydude 10 11,072 01/19/2016, 03:14 AM Last Post: andydude [split] Understanding Kneser Riemann method andydude 7 8,125 01/13/2016, 10:58 PM Last Post: sheldonison

Users browsing this thread: 1 Guest(s)