Difference between revisions of "File:Qexpmap.jpg"

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

<ref name="factorial">

https://link.springer.com/article/10.3103/S0027134910010029 <br>

https://mizugadro.mydns.jp/PAPERS/2010superfae.pdf (English)<br>

https://mizugadro.mydns.jp/PAPERS/2010superfar.pdf (Russian)<br>

D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian version: p.8-14)

</ref>

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]]

<ref>

http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002175851&physid=phys63#navi [[Hellmuth Kneser]]. Reelle analytische Lösungen der Gleichung \( φ(φ(x))=e^x \) und verwandter Funktionalgleichungen. Journal für die reine und angewandte Mathematik / Zeitschriftenband (1950) / Artikel / 56 - 67

</ref>

==References==

<references/>

[[Category:Abelfunction]]

[[Category:ArcTetration]]

[[Category:Book]]

[[Category:BookMap]]

[[Category:Hellmuth Kneser]]

[[Category:Iterate]]

[[Category:Superfunction]]

[[Category:Tetration]]