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.

Ethimology of tetration ^[1].

Tetration for base $b\!=\!2$ ^[2].

Tetration for base $b\!=\!\mathrm {e}$ ^[3] and $b=2$ .

Linear and piece-vice approximation of tetration. ^[4] ^[3].

Tetration for $b\!=\!\mathrm {e}$ ^[3]

Solutions of equation $F(z+1)=\exp(F(z))$ : ^[5] ^[3]

Application of tetration ^[6] ^[4] ^[7] ^[2].

Ackermann Function ^[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 $F(z+1)=\exp(F(z))$ in the complex $z$ 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.

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