01/15/2008, 03:52 PM
Some additional ideas:
We can observe, in the various tetrational plots obtained so far showing y = b # x together with y", a kind of strong correlation between y(x) and its second derivative. Would it be possible to try and identify a possible "... simple" relationship between the two? Something like:
F[y(x), y"(x)] = 0.
In this case, we might end with the identification of a "mother" differential equation, the solutions of which, for different "bases", would give the various appropriate tetrational expression.
Very ambitious program! Perhaps the differential equation does not exist, perhaps it exists but it is difficult to be integrated, perhaps the problem is very simple. Who knows!?! I don't know how to proceed.
GFR
We can observe, in the various tetrational plots obtained so far showing y = b # x together with y", a kind of strong correlation between y(x) and its second derivative. Would it be possible to try and identify a possible "... simple" relationship between the two? Something like:
F[y(x), y"(x)] = 0.
In this case, we might end with the identification of a "mother" differential equation, the solutions of which, for different "bases", would give the various appropriate tetrational expression.
Very ambitious program! Perhaps the differential equation does not exist, perhaps it exists but it is difficult to be integrated, perhaps the problem is very simple. Who knows!?! I don't know how to proceed.
GFR
