• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 periodic ... tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 08/09/2010, 08:55 PM i had some ideas relating tetration and superfunctions in general to the following properties : A) f(z) is Coo and Im f(z) is periodic. B) f(z) is Coo and Re f(z) is periodic. C) A) and B) but f(z) is not periodic. what is known about functions satisfying A) B) or C) ? anything special about them ? are there series expansions only valid for such functions ? tommy1729 Ultimate Fellow Posts: 1,493 Threads: 356 Joined: Feb 2009 08/11/2010, 04:59 PM nothing known about them ? i know my question is a bit vague , but im looking for questions rather than answers i guess sheldonison Long Time Fellow Posts: 683 Threads: 24 Joined: Oct 2008 08/11/2010, 06:50 PM (08/09/2010, 08:55 PM)tommy1729 Wrote: i had some ideas relating tetration and superfunctions in general to the following properties : A) f(z) is Coo and Im f(z) is periodic. B) f(z) is Coo and Re f(z) is periodic. C) A) and B) but f(z) is not periodic. what is known about functions satisfying A) B) or C) ? anything special about them ? are there series expansions only valid for such functions ?I think the Taylor series expansions are usually generated by a matrix. When the superfunction is generated from the fixed point of L for that base, then you have a limit equation, which can indirectly be used to generate a Taylor series. Henryk posted something the other day, that might be relevant (true or false logarithm). But in general, I don't think much is known about generating the Taylor series terms in a closed form. I don't know any cases where Re f(z) is periodic. Im f(z) is periodic for bases

 Possibly Related Threads... Thread Author Replies Views Last Post On the $$2 \pi i$$-periodic solution to tetration, base e JmsNxn 0 324 09/28/2021, 05:44 AM Last Post: JmsNxn A compilation of graphs for the periodic real valued tetrations JmsNxn 1 562 09/09/2021, 04:37 AM Last Post: JmsNxn Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 2,203 09/09/2019, 10:55 PM Last Post: tommy1729 Periodic analytic iterations by Riemann mapping tommy1729 1 4,640 03/05/2016, 10:07 PM Last Post: tommy1729 Can sexp(z) be periodic ?? tommy1729 2 7,166 01/14/2015, 01:19 PM Last Post: tommy1729 [2014] Uniqueness of periodic superfunction tommy1729 0 3,567 11/09/2014, 10:20 PM Last Post: tommy1729 almost periodic musing tommy1729 1 4,060 06/17/2014, 12:24 PM Last Post: tommy1729 periodic equation tommy1729 0 4,442 07/18/2011, 11:13 PM Last Post: tommy1729 Periodic functions that are periodic not by addition JmsNxn 0 4,054 04/17/2011, 09:54 PM Last Post: JmsNxn closed form for regular superfunction expressed as a periodic function sheldonison 31 53,149 09/09/2010, 10:18 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)