Difference between revisions of "File:Qexpmap.jpg"
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| − | [[Complex map]] of function [[square root of exponential]] |
+ | [[Complex map]] of function [[square root of exponential]], \( \varphi=\sqrt{\exp} \) |
<ref> |
<ref> |
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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> |
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| + | Function \( \varphi(z) = \mathrm{tet}(1/2+\mathrm{ate}(z)) = \exp^{1/2}(z)\) |
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| + | |||
| + | appears as solution of equation |
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| + | |||
| + | \( |
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| + | \varphi(\varphi(z))=\exp(z) |
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| + | \) |
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| + | |||
| + | Existence of this function is shown in 1950 by [[Hellmuth Kneser]] |
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| + | <ref> |
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| + | 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> |
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==References== |
==References== |
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<references/> |
<references/> |
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[[Category:Abelfunction]] |
[[Category:Abelfunction]] |
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| + | [[Category:ArcTetration]] |
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[[Category:Book]] |
[[Category:Book]] |
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[[Category:BookMap]] |
[[Category:BookMap]] |
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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
- ↑ http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf D.Kouznetsov1, H.Trappmann. Superfunctions and sqrt of Factorial. (2010)
- ↑ 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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