Hi -
concerning the iteration of the function f(x)=exp(x)-1 I came across the remark of Erdös & Jabotinsky, that due to I.N.Baker a fractional version f°h(x) would not exist. This was stumbling me, since I just had computed lots of nice values for those iterates... In the refered article Baker actually proves that only integer iterates have positive radius of convergence.
Well - phew - with this I can live better than with the Erdös/Jabotinsky-statement.
I've just uploaded some tables, which may illustrate the problem as stated by Baker and give some more specific insight.
No big affair, again, but may be leading into deeper consideration.
see http://go.helms-net.de/math/tetdocs/html...ration.htm
[update]
Compare also my earlier article with a consideration for the half-iterate at http://go.helms-net.de/math/tetdocs/Coef...ration.htm
[/update]
Gottfried
P.s. The article of Baker is online at digicenter university of göttingen.
concerning the iteration of the function f(x)=exp(x)-1 I came across the remark of Erdös & Jabotinsky, that due to I.N.Baker a fractional version f°h(x) would not exist. This was stumbling me, since I just had computed lots of nice values for those iterates... In the refered article Baker actually proves that only integer iterates have positive radius of convergence.
Well - phew - with this I can live better than with the Erdös/Jabotinsky-statement.
I've just uploaded some tables, which may illustrate the problem as stated by Baker and give some more specific insight.
No big affair, again, but may be leading into deeper consideration.
see http://go.helms-net.de/math/tetdocs/html...ration.htm
[update]
Compare also my earlier article with a consideration for the half-iterate at http://go.helms-net.de/math/tetdocs/Coef...ration.htm
[/update]
Gottfried
P.s. The article of Baker is online at digicenter university of göttingen.
Gottfried Helms, Kassel
