Tetration/Bibliography: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Dmitrii Kouznetsov
(If the structure is correct, I add more refs)
imported>Dmitrii Kouznetsov
(update refs for base e)
Line 15: Line 15:


Tetration for base <math>b\!=\!\mathrm{e}</math>
Tetration for base <math>b\!=\!\mathrm{e}</math>
<ref name="k">D.Kouznetsov. Solutions of <math>F(z+1)=\exp(F(z))</math> in the complex <math>z</math>plane. [[Mathematics of Computation]], 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf</ref>
<ref name="k">
{{cite journal
|author=D.Kouznetsov.
|title=Solutions of <math>F(z\!+\!1)=\exp(F(z))</math> in the complex <math>z</math>plane.  
|journal=[[Mathematics of Computation]],
|year=2009
|volume=78
|pages=1647-1670
|url= http://www.ams.org/mcom/2009-78-267/S0025-5718-09-02188-7/home.html
|preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
|doi=10.1090/S0025-5718-09-02188-7
}}preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
</ref><ref name="vladie">
{{cite journal
|author=D.Kouznetsov.
|title=Superexponential as special function.
|journal=[[Vladikavkaz Mathematical Journal]], in press.
}}
Preprint, English version: http://www.ils.uec.ac.jp/~dima/PAPERS/2009vladie.pdf
</ref>


<!--
Linear and piece-vice approximation of tetration.
Linear and piece-vice approximation of tetration.
<ref name="uxp">
<ref name="uxp">
Line 25: Line 45:
Tetration for <math>b\!=\!\mathrm{e}</math>
Tetration for <math>b\!=\!\mathrm{e}</math>
<ref name="k">D.Kouznetsov. Solutions of <math>F(z+1)=\exp(F(z))</math> in the complex <math>z</math>plane. [[Mathematics of Computation]], 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf</ref>
<ref name="k">D.Kouznetsov. Solutions of <math>F(z+1)=\exp(F(z))</math> in the complex <math>z</math>plane. [[Mathematics of Computation]], 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf</ref>
!-->


Solutions of equation <math>F(z+1)=\exp(F(z))</math>:
Other solutions of equation <math>F(z+1)=\exp(F(z))</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 '('(x)) = ex 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>
<ref name="k">D.Kouznetsov. Solutions of <math>F(z+1)=\exp(F(z))</math> in the complex <math>z</math>plane. [[Mathematics of Computation]], 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf</ref>


Application of tetration <ref>
Application of tetration <ref>
Line 56: Line 76:
</ref>.
</ref>.


Additional literature around
About iterations:
<ref>A.Knoebel. ”Exponentials Reiterated.” Amer. Math. Monthly 88 (1981), 235-252.</ref>
<ref>{{cite journal
|author=A.Knoebel
|title=Exponentials Reiterated
|journal=Amer. Math. Monthly
|volume=88
|year=1981
|pages=235-252
}}</ref>
 




<references/>
<references/>

Revision as of 22:37, 15 November 2009

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

Ethimology of tetration [1].

Tetration for base [2].

Tetration for base [3][4]


Other solutions of equation : [5]

Application of tetration [6] [7] [8] [2].

Ackermann Function [8] [2].

About iterations: [9]


  1. ↑ R.L.Goodstein (1947). "Transfinite ordinals in recursive number theory". Journal of Symbolic Logic 12.
  2. ↑ 2.0 2.1 2.2 D.Kouznetsov. Ackermann functions of complex argument. Preprint of the Institute for Laser Science, 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 Cite error: Invalid <ref> tag; name "k2" defined multiple times with different content
  3. ↑ D.Kouznetsov. (2009). "Solutions of in the complex plane.". Mathematics of Computation, 78: 1647-1670. DOI:10.1090/S0025-5718-09-02188-7. Research Blogging. preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
  4. ↑ D.Kouznetsov.. "Superexponential as special function.". Vladikavkaz Mathematical Journal, in press.. Preprint, English version: http://www.ils.uec.ac.jp/~dima/PAPERS/2009vladie.pdf
  5. ↑ H.Kneser. “Reelle analytische L¨osungen der Gleichung '('(x)) = ex und verwandter Funktionalgleichungen”. Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67.
  6. ↑ P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
  7. ↑ M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)
  8. ↑ 8.0 8.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
  9. ↑ A.Knoebel (1981). "Exponentials Reiterated". Amer. Math. Monthly 88: 235-252.
Retrieved from "https://citizendium.org/wiki/index.php?title=Tetration/Bibliography&oldid=550902"