Difference between revisions of "File:Expe1emapT1000.jpg"

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{{oq|Expe1emapT1000.jpg|Original file ‎(2,361 × 2,333 pixels, file size: 1.35 MB, MIME type: image/jpeg) }}
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[[Complex map]] of [[exponential]] to [[base e1e]], $b=\exp(1/e)$
  
   
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[[Complex map]] of [[exponential]] to [[base e1e]], \(b\!=\!\exp(1/\mathrm e)\):
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$u+\mathrm i v = \exp_b(x+\mathrm i y$
  
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\[
  ⚫
u+\mathrm i v = \exp_b(x+\mathrm i y)
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\]
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This map is used as Fig.10.2 at page 118 of book
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«[[Superfunctions]]», 2020 <ref>
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https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862 Dmitrii Kouznetsov. [[Superfunctions]]: Non-integer iterates of holomorphic functions. [[Tetration]] and other [[superfunction]]s. Formulas,algorithms,tables,graphics - 2020/7/28
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</ref><ref>https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov (2020). [[Superfunctions]]: Non-integer iterates of holomorphic functions. [[Tetration]] and other [[superfunction]]s. Formulas, algorithms, tables, graphics. Publisher: [[Lambert Academic Publishing]].
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</ref>
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in order to remind that exponential is periodic function.
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and explain better which function is treated as [[Transfer function]].
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==References==
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{{ref}}
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{{fer}}
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==Keywords==
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«[[Base e1e]]»,
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«[[Exotic iterations]]»,
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«[[Fixed pount]]»,
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«[[Regular iteraiton]]»,
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«[[Superfunctions]]»,
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«[[Transfer function]]»,
   
 
[[Category:Base e1e]]
  
[[Category:Base e1e]]
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[[Category:Complex map]]
  
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[[Category:Exp]]
  
 
[[Category:Book]]
  
[[Category:Book]]
 
[[Category:BookMap]]
  
[[Category:BookMap]]
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[[Category:Complex map]]
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[[Category:Exotic iteration]]
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[[Category:Exp]]
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[[Category:Transfer function]]
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[[Category:Superfunction]]

Latest revision as of 16:09, 23 August 2025


Complex map of exponential to base e1e, \(b\!=\!\exp(1/\mathrm e)\):

\[ u+\mathrm i v = \exp_b(x+\mathrm i y) \]

This map is used as Fig.10.2 at page 118 of book «Superfunctions», 2020 [1][2] in order to remind that exponential is periodic function. and explain better which function is treated as Transfer function.

References

  1. ↑ https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862 Dmitrii Kouznetsov. Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics - 2020/7/28
  2. ↑ https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov (2020). Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas, algorithms, tables, graphics. Publisher: Lambert Academic Publishing.

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