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 Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 05/27/2008, 08:10 AM (This post was last modified: 05/27/2008, 08:11 AM by Ivars.) Gottfried Wrote:Refering to the header of this thread and your obvious love to iteration and trajectories, I challenge you to compute the alternating sum of all the intermediate steps of the trajectory I, 2^I, 2^(2^I), 2^(2^(2^I)... AS(2,I) = I - 2^I + 2^2^I - 2^2^2^I + ... -... = ?? My proposal is AS(2,I) = -0.440033096027+0.928380628227*I What do you think? Gottfried I can only say it diverges, and I understand You want me to find a method to sum it and a result. Unfortunately, I can not do it yet, but I am interested in 2^I in general and divergent series as well as they might be doing the same as tetration-somehow sending real numbers to complex domain , though the example I made with infinite logarithms ended in a kind of disaster as every base b ( except h(0) and h(1)) atracted to single value -W(-1). So let us keep Your result in mind while learn the basics in my strange ways-backwards Ivars « Next Oldest | Next Newest »

 Messages In This Thread Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/19/2008, 09:02 PM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/20/2008, 06:12 AM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 06:43 AM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 04:46 PM RE: Calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 04:59 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 08:36 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/20/2008, 09:08 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/21/2008, 06:33 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/21/2008, 10:29 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/22/2008, 08:13 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/23/2008, 06:51 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/23/2008, 11:44 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/24/2008, 08:13 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by bo198214 - 05/24/2008, 08:55 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/24/2008, 04:09 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/25/2008, 08:28 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/25/2008, 10:48 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/25/2008, 06:08 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/25/2008, 10:12 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/26/2008, 07:43 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/26/2008, 09:01 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/26/2008, 10:30 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/26/2008, 01:11 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/25/2008, 10:51 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/27/2008, 08:10 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 05/27/2008, 09:23 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Ivars - 05/27/2008, 11:45 AM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by tommy1729 - 04/11/2014, 10:54 PM RE: Fractals from calculations of 2^I, 2^(2^I), 2^(2^(2^I).. a^(a^(...a^I) - by Gottfried - 04/12/2014, 01:10 AM

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