On Real Analytic Tetration

©2007 Andrew Robbins
Abstract We review the theory of infinitely iterated exponentials and E()SUP(V(x))−1 and derive a relationship between the analytic iteration of E()SUP(V(x))−1 and tetration.

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Solving for the Analytic Piecewise Extension
of Tetration and the Super-logarithm

©2005 Andrew Robbins
Abstract An overview of previous extensions of tetration is presented. Specific conditions for differentiability and piecewise continuity are shown. This leads to a way of generating approximations of the super-logarithm. These approximations are shown to converge to a function that satisfies two basic properties of extensions of tetration.

This paper was broken into parts because of restrictions on file sizes, but now you can get a complete version all in one file:

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