Searching for an asymptotic to exp[0.5]

[JmsNxn]

Well not from Hadamard alone , but from the asymptotes of the zero's yes.

Maybe I'm misinterpreting your response but a huge lemma that hadamard uses in his proof is that:

if \( |f(z)| < C e^{\rho|z|^{\sigma}} \)

then NECESSARILY, (by doing some magic with jensen's formula and some other neat complex analysis), if \( a_j \) are the zeroes of f

\( \sum_{j=1}^\infty |a_j|^{-(\sigma + \epsilon)} < \infty \)