Tetration/Bibliography

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A list of key readings about Tetration.
Please sort and annotate in a user-friendly manner. For formatting, consider using automated reference wikification.

Etymology of tetration [1].

Tetration for base [2].

Tetration for base [3][4]

Uniqueness of the tetration and arctetration at base [5]

Superexponentials (and the tetration) to base [6]

Superexponentials (and the tetration) for the case , and, in particular, for [7]


Other solutions of equation : [8]

Application of tetration [9] [10] [11] [2].

Ackermann Function [11] [2].

About iterations: [12]

Wiki-resources related to tetration:
http://www.proofwiki.org/wiki/Definition:Tetration
http://tori.ils.uec.ac.jp/TORI/index.php/Tetration

References

  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
  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. (2009). "Superexponential as special function.". Vladikavkaz Mathematical Journal 12 (2): 31-45.
  5. H.Trappmann, D.Kouznetsov. Uniqueness of Analytic Abel Functions in Absence of a Real Fixed Point. Aequationes Mathematicae, v.81, p.65-76 (2011) http://www.springerlink.com/content/u7327836m2850246/ http://tori.ils.uec.ac.jp/PAPERS/2011uniabel.pdf
  6. H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). Mathematics of computation, in preparation, 2011. http://tori.ils.uec.ac.jp/PAPERS/2011e1e.pdf
  7. D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756. http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html http://tori.ils.uec.ac.jp/PAPERS/2010sqrt2.pdf
  8. H.Kneser. “Reelle analytische L¨osungen der Gleichung und verwandter Funktionalgleichungen”. Journal fur die reine und angewandte Mathematik, 187 (1950), 56-67.
  9. P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
  10. M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)
  11. 11.0 11.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
  12. A.Knoebel (1981). "Exponentials Reiterated". Amer. Math. Monthly 88: 235-252.