Difference between revisions of "File:Qexpmap.jpg"

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[[Complex map]] of function [[square root of exponential]].
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[[Complex map]] of function [[square root of exponential]], \( \varphi=\sqrt{\exp} \)
 
<ref>
 
<ref>
 
http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf
 
http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf
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</ref>
 
</ref>
   
  +
Function \( \varphi(z) = \mathrm{tet}(1/2+\mathrm{ate}(z)) = \exp^{1/2}(z)\)
  +
  +
appears as solution of equation
  +
  +
\(
  +
\varphi(\varphi(z))=\exp(z)
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\)
  +
  +
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
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</ref>
 
==References==
 
==References==
 
<references/>
 
<references/>
   
 
[[Category:Abelfunction]]
 
[[Category:Abelfunction]]
  +
[[Category:ArcTetration]]
 
[[Category:Book]]
 
[[Category:Book]]
 
[[Category:BookMap]]
 
[[Category:BookMap]]

Revision as of 23:16, 30 November 2019

Complex map of function square root of exponential, \( \varphi=\sqrt{\exp} \) [1]

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 [2]

References

  1. http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf D.Kouznetsov1, H.Trappmann. Superfunctions and sqrt of Factorial. (2010)
  2. 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

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