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+--- Thread: A f(x) = f(g(x)) + f(h(x)) (/showthread.php?tid=941)
A f(x) = f(g(x)) + f(h(x)) - tommy1729 - 12/10/2014
Together with my friend mick We came to consider the following ( after thinking about fake function theory ) :
Let a given A be 0 < A < 2.
tommy-mick 3 entires Conjecture :
For any real entire f(x) there exist real entire g(x) and h(x) such that
A f(x) = f(g(x)) + f(h(x))
or
A f(x) = f(g(x)) - f(h(x))
is satisfied.
The idea of positive derivatives and the alike led to many disputes
( and related to fake function theory naturally )
Im tempted to mention that I considered some matrix ideas such as Carleman and some ideas from Gottfried.
( Though the ideas I tried based on Gottfried's ideas seem to have trouble with convergeance ... )
But with no result so far.
Its possible that I posted this before in the past and maybe it has been considered 100 years ago.
I believe the real intresting things happen when we develop ( or rediscover ) the tools to solve this.
This is because this problem is a cornerstone ; many numerical methods and theoretical ideas I had - but did not publish - depend on the truth of this and a way to compute it.
Bye the way you can vote for mick on MSE , he put himself as a candidate for moderator.
Since he is probably the only young MSE user into tetration with a rep above 2000 he might be the man ( boy
) to defend/judge tetration Q&A.My apologies if im wrong : maybe some other users here or on MSE are young and have rep above 2000 too.
( Sheldon and Gottfried are on MSE but they are older , perhaps im forgetting balarka or galathaea or ... )
regards
tommy1729