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+--- Thread: periodic ... (/showthread.php?tid=488)
periodic ... - tommy1729 - 08/09/2010
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 ?
RE: periodic ... - tommy1729 - 08/11/2010
nothing known about them ?
i know my question is a bit vague , but im looking for questions rather than answers i guess
RE: periodic ... - sheldonison - 08/11/2010
(08/09/2010, 08:55 PM)tommy1729 Wrote: i had some ideas relating tetration and superfunctions in general to the following properties :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.
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 don't know any cases where Re f(z) is periodic. Im f(z) is periodic for bases<eta.
- Sheldon
RE: periodic ... - tommy1729 - 08/11/2010
(08/11/2010, 06:50 PM)sheldonison Wrote: I don't know any cases where Re f(z) is periodic. Im f(z) is periodic for bases<eta.
- Sheldon
im i going crazy or is it really that simple ?
you say you dont know a case with Re periodic.
but you do know a case where Im is periodic.
if you multiply your Im solution by i , you get a Re periodic.
shoot me if that is wrong.
thanks for your reply though
the rest made sense to me :p
i was thinking about the fixpoints being all conjugate of each other and expansion of fixp1 = expansion of fixp2 as some sort of condition ...
also the above comment by you and me seem to be focused on superfunctions.
but im also intrested in the functions not defined as superfunctions ( or even NO superfunctions [ not every f is a superfunction ] ) and how THEIR superfunctions behave if they have re/im periodic.
regards
tommy1729
RE: periodic ... - bo198214 - 08/13/2010
(08/11/2010, 07:22 PM)tommy1729 Wrote: im i going crazy or is it really that simple ?
you say you dont know a case with Re periodic.
but you do know a case where Im is periodic.
if you multiply your Im solution by i , you get a Re periodic.
and which is then no more a superfunction.
RE: periodic ... - tommy1729 - 08/15/2010
for clarity , im not considering superfunctions with a Re or Im period , but a general entire function with Re or Im periodic.
also i do mean that Im(f(z)) is periodic with Im periodic , not a function that has q i as a period.