09/03/2007, 08:41 PM

bo198214 Wrote:Gottfried Wrote:Quote:However perhaps it could be that is real or generally that is real, which I dont believe. Can someone just compute it?

Hmm, I don't know, whether I understand you correctly. If h=1 then all eigenvalues except the first are zero ( = [1,0,0,....]) and the result is always the same, independent of any power of log(h) since the "height" y of the tower occurs only as exponent of the eigenvalues....

Did I misread something obvious?

As said is not 1 but .

, is the power derivation matrix of (I think this is the transpose of your matrix ), and is (though we can also apply the powerseries directly to ). Hence the power series has as coefficients the first row of (think transposed in your notation).

And now tetration is defined as . We set not .

ok, I misread that as x^^t instead of {h,x}^^t, as in Andrew's notational references. I got it now. If there are only two parameters given as in I automatically assume, that it is {x,1}^^t instead of {<context>,x}^^t. I think I'll have to get used to it now...

Thanks -

Gottfried

Gottfried Helms, Kassel