Tetration > Bibliography

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	A list of key readings about Tetration.

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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]}.

Ackermann Function ^{[7] [2]}.

Additional literature around ^[8]

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. ↑ ^{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. ↑ ^4.0 4.1 M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)
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. ↑ ^7.0 7.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
8. ↑ A.Knoebel. ”Exponentials Reiterated.” Amer. Math. Monthly 88 (1981), 235-252.