Superfunction/Bibliography: Difference between revisions

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{{subpages}}
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==About superfunctions of factorial and <math> \sqrt{!} </math>==
==About superfactorial and <math> \sqrt{!} </math>==


About <math>\sqrt{!}</math>
About <math>\sqrt{!}</math> as logo
<ref name="logo">Logo of the Physics Department of the Moscow State University. (In Russian);
<ref name="logo">Logo of the Physics Department of the Moscow State University. (In Russian);
http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml
http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml
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About superfactorial and <math> \sqrt{!} </math>:
About superfactorial and <math> \sqrt{!} </math>:
<ref name="superfactorial">
<ref name="superfactorial">
  D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Preprint ILS, 2009:
  D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Preprint ILS UEC, 2009:
http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf
http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf
</ref>
</ref>
Line 38: Line 38:
Tetration for base <math>b\!=\!\mathrm{e}</math>
Tetration for base <math>b\!=\!\mathrm{e}</math>
<ref name="kneser">
<ref name="kneser">
H.Kneser. “Reelle analytische L¨osungen der Gleichung '('(x)) = ex und verwandter Funktionalgleichungen”.
H.Kneser. “Reelle analytische L¨osungen der Gleichung  
<math>\varphi(\varphi(x)) = \exp(x)</math> und verwandter Funktionalgleichungen”.
Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67.
Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67.
</ref>
</ref>
Line 55: Line 56:
</ref>
</ref>


Tetration for base <math>b\!=\!2</math>
Tetrational to base <math>b\!=\!2</math>
<ref name="k2">D.Kouznetsov. Ackermann functions of complex argument. Preprint of the Institute for Laser Science, UEC, 2008.
<ref name="k2">D.Kouznetsov. Ackermann functions of complex argument. Preprint ILS UEC, 2008.
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf</ref>.
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf</ref>.
Superexponentials (and, in particular the tetrational)
to base <math>b\!=\!\sqrt{2}</math>
<ref>
D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Preprint ILS UEC,
http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf
</ref>


Linear and piece-vice approximation of tetration
Linear and piece-vice approximation of tetration
<ref name="uxp">
<ref name="uxp">
{{cite hournal
{{cite journal
|author=M.H.Hooshmand
|author=M.H.Hooshmand
|title=Ultra power and ultra exponential functions
|title=Ultra power and ultra exponential functions
Line 85: Line 93:
D.Kouznetsov. Ackermann functions of complex argument.
D.Kouznetsov. Ackermann functions of complex argument.
Preprint ILS UEC, 2008,
Preprint ILS UEC, 2008,
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf
</ref>.
<ref name="k2">
D.Kouznetsov. Ackermann functions of complex argument. Preprint ILS UEC, 2008
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf
</ref>.
</ref>.

Revision as of 01:34, 14 August 2009

This article is developing and not approved.
 Main Article
 Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
https://en.citizendium.org/wiki/index.php?title=Superfunction/Bibliography&printable=yes
A list of key readings about Superfunction.
Please sort and annotate in a user-friendly manner. For formatting, consider using automated reference wikification.

About superfactorial and

About as logo [1] [2] [3]

About superfactorial and : [4]

About superexponentias and

Tetration for base [5] [6]

Tetrational to base [7].

Superexponentials (and, in particular the tetrational) to base [8]

Linear and piece-vice approximation of tetration [9]

Application of tetration [10] [9] [11] [7].

Additional literature around

Reiterated exponential [12].

Ackermann Function [11]


  1. ↑ Logo of the Physics Department of the Moscow State University. (In Russian); http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml
  2. ↑ V.P.Kandidov. About the time and myself. (In Russian) http://ofvp.phys.msu.ru/pdf/Kandidov_70.pdf:

    По итогам студенческого голосования победителями оказались значок с изображением

    рычага, поднимающего Землю, и нынешний с хорошо известной эмблемой в виде корня из факториала, вписанными в букву Ф. Этот значок, созданный студентом кафедры биофизики А.Сарвазяном, привлекал своей простотой и выразительностью. Тогда эмблема этого значка подверглась жесткой критике со стороны руководства факультета, поскольку она не имеет физического смысла, математически абсурдна и идеологически бессодержательна.

  3. ↑ 250 anniversary of the Moscow State University. (In Russian) ПЕРВОМУ УНИВЕРСИТЕТУ СТРАНЫ - 250! http://nauka.relis.ru/11/0412/11412002.htm

    На значке физфака в букву "Ф" вписано стилизованное изображение корня из факториала (√!) - выражение, математического смысла не имеющее.

  4. ↑ D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Preprint ILS UEC, 2009: http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf
  5. ↑ H.Kneser. “Reelle analytische L¨osungen der Gleichung und verwandter Funktionalgleichungen”. Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67.
  6. ↑ D.Kouznetsov (2008). "Solutions of in the complex plane.". Mathematics of Computation 78: 1647-1670. DOI:10.1090/S0025-5718-09-02188-7. Research Blogging.
  7. ↑ 7.0 7.1 D.Kouznetsov. Ackermann functions of complex argument. Preprint ILS UEC, 2008. http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf Cite error: Invalid <ref> tag; name "k2" defined multiple times with different content
  8. ↑ D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Preprint ILS UEC, http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf
  9. ↑ 9.0 9.1 M.H.Hooshmand (2006). "Ultra power and ultra exponential functions". Integral Transforms and Special Functions 17 (8): 549-558. Cite error: Invalid <ref> tag; name "uxp" defined multiple times with different content
  10. ↑ P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
  11. ↑ 11.0 11.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
  12. ↑ A.Knoebel. ”Exponentials Reiterated.” Amer. Math. Monthly 88 (1981), 235-252.
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