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May 27, 2018 at 1:51 comment added fedja You can do it in a bit cheaper way if you notice that for $s<1$ any function in $G_s$ is entire of a certain order of growth and that that order can be read from the Taylor series coefficients at $0$. In particular, $G_0$ allows only exponential growth while it is fairly clear that $e^{e^z}$ goes up a bit faster.
Apr 26, 2018 at 21:24 review First posts
Apr 26, 2018 at 21:26
Apr 26, 2018 at 21:24 history answered arriopolis CC BY-SA 3.0