07/24/2008, 02:25 PM

Hi -

I am currently reviewing the problem of divergence of powerseries (for the fractional iteration of Ut°h(x), but real bases).

First I produced some plots with few different bases to get a better overview over the general characterisitcs of the divergence of the powerseries.

Today I found a start to overcome that nasty type of divergence: using a Stirling-transform (as I call it at the moment) of the powerseries I get nicely convergent series even for the fractional case (just had only time to check this for one (divergent) base b=exp(2)). This is a big progress for my implementation of diagonalization!

Look at

http://go.helms-net.de/math/tetdocs/Coef...Height.htm

Gottfried

I am currently reviewing the problem of divergence of powerseries (for the fractional iteration of Ut°h(x), but real bases).

First I produced some plots with few different bases to get a better overview over the general characterisitcs of the divergence of the powerseries.

Today I found a start to overcome that nasty type of divergence: using a Stirling-transform (as I call it at the moment) of the powerseries I get nicely convergent series even for the fractional case (just had only time to check this for one (divergent) base b=exp(2)). This is a big progress for my implementation of diagonalization!

Look at

http://go.helms-net.de/math/tetdocs/Coef...Height.htm

Gottfried

Gottfried Helms, Kassel