Is bounded tetration is analytic in the base argument?

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Is bounded tetration is analytic in the base argument? - Printable Version

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Is bounded tetration is analytic in the base argument? - JmsNxn - 01/02/2017

A very simple question I can't find in the scattered tetration literature.

If $1 < \alpha < e^{1/e}$ is $^z\alpha$ analytic in $\alpha$ ? I.e: is it expandable into a Taylor series in $\alpha$ depending on $z$ about each $\alpha_0 \in (1,\eta)$ ?