Tetration/Bibliography: Difference between revisions
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<ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. [[Mathematische Annalen]] | <ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. [[Mathematische Annalen]] | ||
99(1928), 118-133</ref> | 99(1928), 118-133</ref> | ||
<ref name="k2" | <ref name="k2"/>. | ||
Ackermann Function | Ackermann Function | ||
<ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. [[Mathematische Annalen]] | <ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. [[Mathematische Annalen]] | ||
99(1928), 118-133</ref> | 99(1928), 118-133</ref> | ||
<ref name="k2" | <ref name="k2"/>. | ||
About iterations: | About iterations: | ||
Latest revision as of 10:10, 16 September 2024
- Please sort and annotate in a user-friendly manner. For formatting, consider using automated reference wikification.
Etymology of tetration [1].
Tetration for base [2].
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].
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
- ↑ R.L.Goodstein (1947). "Transfinite ordinals in recursive number theory". Journal of Symbolic Logic 12.
- ↑ 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
- ↑ 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
- ↑ D.Kouznetsov. (2009). "Superexponential as special function.". Vladikavkaz Mathematical Journal 12 (2): 31-45.
- ↑ 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
- ↑ 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
- ↑ 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
- ↑ H.Kneser. “Reelle analytische L¨osungen der Gleichung und verwandter Funktionalgleichungen”. Journal fur die reine und angewandte Mathematik, 187 (1950), 56-67.
- ↑ P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
- ↑ M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)
- ↑ 11.0 11.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
- ↑ A.Knoebel (1981). "Exponentials Reiterated". Amer. Math. Monthly 88: 235-252.
