File:Qexpmap.jpg

Complex map of function square root of exponential, \( \varphi=\sqrt{\exp} \)

Function \( \varphi(z) = \mathrm{tet}(1/2+\mathrm{ate}(z)) = \exp^{1/2}(z)\)

appears as solution of equation

\( \varphi(\varphi(z))=\exp(z) \)

Existence of this function is shown in 1950 by Hellmuth Kneser