01/29/2011, 03:26 PM
well im sorry too Bo.
but it seems you missed the point.
lim n -> oo log^[n] ( exp^[n] (x) ) also doesnt have a somewhere non-zero convergence radius.
but clearly 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.
but it seems you missed the point.
lim n -> oo log^[n] ( exp^[n] (x) ) also doesnt have a somewhere non-zero convergence radius.
but clearly 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.