Is bounded tetration is analytic in the base argument? - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Is bounded tetration is analytic in the base argument? (/showthread.php?tid=1109) 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 $\alpha_0 \in (1,\eta)$?