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