Nowhere analytic superexponential convergence

[bo198214]

i just wrote *complex* - analytic to informally point out the difference with real-analytic.
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now knowing that , you might wanna read my post again ?

Sorry, tommy your post makes no sense then. You say its not analytic, but real-analytic. Its not analytic where? If it is real analytic then it is analytic on a neighborhood of the real axis/interval.

as i understood sheldon , he means " nowhere-analytic " rather than " nowhere-analytic " on the real axis.

The function is only defined on the real axis, of course he speaks about the real axis.

tommysexp is real-analytic.

I dont think so. Everything is pointing to the opposite: nowhere analytic on the real axis. This is because the sequence of functions gets singularities nearer and denser around the real axis (convergence radius shrinking to 0). This is no proof, but makes it quite unlikely that the limit function has somewhere non-zero convergence radius.