01/29/2011, 08:59 PM
well according to Bo it is not real-analytic and it doesnt have a radius , and according to mike it does have a radius.
a radius is usually considered a radius of a circle.
for reals we usually talk about intervals.
so opinions and/or terminology differs , i hope at least everyone agrees on :
on the real line f(x) = lim n -> oo log^[n] ( exp^[n] (x) ) is real-analytic because it simply reduces to f(x) = x for real x , which is clearly real-analytic.
and for real-analytic i prefer to say : analytic on an interval , rather than a radius , for imho a nonzero-radius is for analytic taylor series - analytic on on a disk on the complex plane with nonzero-radius.
a radius is usually considered a radius of a circle.
for reals we usually talk about intervals.
so opinions and/or terminology differs , i hope at least everyone agrees on :
on the real line f(x) = lim n -> oo log^[n] ( exp^[n] (x) ) is real-analytic because it simply reduces to f(x) = x for real x , which is clearly real-analytic.
and for real-analytic i prefer to say : analytic on an interval , rather than a radius , for imho a nonzero-radius is for analytic taylor series - analytic on on a disk on the complex plane with nonzero-radius.