Tetration/Bibliography: Difference between revisions
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imported>Dmitrii Kouznetsov (draft) |
imported>Dmitrii Kouznetsov (If the structure is correct, I add more refs) |
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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">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> | ||
Linear and piece-vice approximation of tetration. | Linear and piece-vice approximation of tetration. | ||
Revision as of 04:45, 5 November 2008
- 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]
Linear and piece-vice approximation of tetration. [4] [3].
Tetration for [3]
Solutions of equation : [5] [3]
Application of tetration [6] [4] [7] [2].
Additional literature around [8]
- ↑ 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 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 - ↑ 3.0 3.1 3.2 3.3 D.Kouznetsov. Solutions of in the complex plane. Mathematics of Computation, 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
- ↑ 4.0 4.1
M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and
Special Functions 17 (8), 549-558 (2006) Cite error: Invalid
<ref>tag; name "uxp" defined multiple times with different content - ↑ 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.
- ↑ P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
- ↑ 7.0 7.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
- ↑ A.Knoebel. ”Exponentials Reiterated.” Amer. Math. Monthly 88 (1981), 235-252.
