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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]^[4]

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

Application of tetration ^[6] ^[7] ^[8] ^[2].

Ackermann Function ^[8] ^[2].

About iterations: ^[9]

↑ 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
↑ D.Kouznetsov. (2009). "Solutions of $F(z\!+\!1)=\exp(F(z))$ in the complex $z$ 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.. "Superexponential as special function.". Vladikavkaz Mathematical Journal, in press.. Preprint, English version: http://www.ils.uec.ac.jp/~dima/PAPERS/2009vladie.pdf
↑ 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.
↑ M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)
↑ ^8.0 ^8.1 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.

[good-1] R.L.Goodstein (1947). "Transfinite ordinals in recursive number theory". Journal of Symbolic Logic 12.

[k2-2] 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 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

[k-3] D.Kouznetsov. (2009). "Solutions of $F(z\!+\!1)=\exp(F(z))$ in the complex $z$ 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

[vladie-4] D.Kouznetsov.. "Superexponential as special function.". Vladikavkaz Mathematical Journal, in press.. Preprint, English version: http://www.ils.uec.ac.jp/~dima/PAPERS/2009vladie.pdf

[kneser-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.

[uxp-7] M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and Special Functions 17 (8), 549-558 (2006)

[a-8] 8.0 ^8.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133

[9] A.Knoebel (1981). "Exponentials Reiterated". Amer. Math. Monthly 88: 235-252.

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