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 The upper superexponential bo198214 Administrator Posts: 1,395 Threads: 91 Joined: Aug 2007 05/11/2009, 01:21 PM (This post was last modified: 05/11/2009, 01:22 PM by bo198214.) (05/11/2009, 12:55 PM)sheldonison Wrote: Are $F_{2,3}$ and $F_{4,3}$ the same two functions in the Bummer post? yes. They are also related to the earlier post which considers the two regular half iterates of $\exp_{\sqrt{2}}$ on the interval (2,4), these are: ${\exp_{\sqrt{2}}}^{[1/2]}(z)=F_{2,3}(1/2+F_{2,3}^{-1}(z))$ and ${\exp_{\sqrt{2}}}^{[1/2]}(z)=F_{4,3}(1/2+F_{4,3}^{-1}(z))$. Quote:Could you comment on how the behavior of the two functions differ in the complex plane? ... Do they have the same periodicity? ... Does only one have singularities? $F_{4,3}$ is entire, has period $2\pi i/\ln(2\ln(2))$. $F_{2,3}$ is not entire, has period $2\pi i/\ln(\ln(2))$. Dmitrii can perhaps tell more about the singularities. Quote: Do both functions have the same values at z=+/-i*infinity? They have no limit along the imaginary axis because they are imaginary periodic. Quote:Given that $F_{2,3}(z)= F_{4,3}(z)$ at all integer values of z, then can these two functions be expressed in terms of each other, where $F_{2,3}= F_{4,3}(x+\theta(x))$? Is the $\theta(x)$ function analytic? Yes, $\theta(z)=F_{4,3}^{-1} ( F_{2,3}(z)) -z$ is analytic, though may somewhere have non-real singularities. « Next Oldest | Next Newest »

 Messages In This Thread The upper superexponential - by bo198214 - 03/29/2009, 11:23 AM RE: The upper superexponential - by andydude - 03/31/2009, 04:29 AM RE: The upper superexponential - by sheldonison - 04/03/2009, 03:06 PM RE: The upper superexponential - by bo198214 - 04/03/2009, 04:22 PM RE: The upper superexponential - by sheldonison - 04/05/2009, 12:45 PM RE: The upper superexponential - by bo198214 - 04/06/2009, 06:35 AM RE: The upper superexponential - by Kouznetsov - 05/10/2009, 02:13 PM RE: The upper superexponential - by sheldonison - 05/11/2009, 12:55 PM RE: The upper superexponential - by bo198214 - 05/11/2009, 01:21 PM RE: The upper superexponential - by sheldonison - 05/11/2009, 08:12 PM RE: The upper superexponential - by bo198214 - 05/11/2009, 08:31 PM RE: The upper superexponential - by Kouznetsov - 05/12/2009, 08:54 AM RE: The upper superexponential - by bo198214 - 06/01/2009, 07:24 PM RE: The upper superexponential - by tommy1729 - 04/05/2009, 07:05 PM RE: The upper superexponential - by sheldonison - 04/22/2009, 05:02 PM RE: The upper superexponential - by bo198214 - 04/22/2009, 05:34 PM RE: The upper superexponential/eich-value x for h=0? - by Gottfried - 09/18/2009, 04:01 PM

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