01/30/2011, 06:48 PM

(01/29/2011, 11:53 PM)bo198214 Wrote:(01/29/2011, 08:59 PM)tommy1729 Wrote: well according to Bo it is not real-analytic and it doesnt have a radius , and according to mike it does have a radius.

I was not talking about which is for each the identity function. Of course it is real-analytic, even entire.

I was talking about tommysexp construction and the basechange.

In each step it has a radius of convergence, which though diminishes to 0 for .

and here you are wrong.

you say is entire.

it is not.

i suggest you plot MINUS z on the complex plane ; and see ' how entire it actually is '.

in fact even log(exp(z)) is not entire.

hint : log(exp(z)) is periodic and id(z) is not.

regards

tommy1729