Complex Tetration and Ackermann Function

[Daniel]

I have Mathematica resources at http://tetration.org/Resources/Files/Mathematica/ . SchroederSummations.nb implements what I call Schroeder Summations which is the current basis of my work with the complex Ackermann function. Convergence is predicated on using the proper simplification for the geometrical progressions which results in the different types of fixed points (hyperbolic, parabolic, ...). The parabolic case b=e^(1/e) simplifies to a polynomial expansion giving uniqueness where all other cases simplify to expansions based on the powers of the log of the fixed point.