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 The upper superexponential sheldonison Long Time Fellow Posts: 683 Threads: 24 Joined: Oct 2008 05/11/2009, 08:12 PM (This post was last modified: 05/11/2009, 08:18 PM by sheldonison.) (05/11/2009, 01:21 PM)bo198214 Wrote: $F_{4,3}$ is entire, has period $2\pi i/\ln(2\ln(2))$. $F_{2,3}$ is not entire, has period $2\pi i/\ln(\ln(2))$. .... They have no limit along the imaginary axis because they are imaginary periodic.When I first looked at Dimitrii's graphs in "Bummer", I didn't realize that the two functions were completely different functions in the imaginary plane, and have different imaginary periods! What I noticed was one had cut points, and the other had fractal behavior. Are the imaginary periods exactly repeating copies? (05/10/2009, 02:13 PM)Kouznetsov Wrote: Functions $F$ above are related: $F_{2,3}$ can be expressed through $F_{2,1}$ and $F_{4,3}$ can be expressed through $F_{4,5}$ with some complex constant ofsets of the arguments. The fractal behavior of $F_{4,3}$ is $F_{4,5}$ increasing to infinity via tetration, except it is occurring at the i=imaginary_period/2 line, with real values! But otherwise, the fractal behavior is as one would expect! It sounds as though the conversions are as simple as: $F_{2,1}(z)=F_{2,3}(z+\text{complexoffset1})$ $F_{4,5}(z)=F_{4,3}(z+\text{complexoffset2})$ $F_{2,3}(z)= F_{4,3}(z+\theta(z))$, Where the complex offset is just a real offset plus half of the imaginary period of each function. This means $\theta$ along with the complex offsets, also allows conversions between $F_{2,1}$ and $F_{4,5}$, the lower superexponential, and the upper superexponential. « 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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