Andrew Robbins' Tetration Extension

[jaydfox]

In the same way that log(0) is indeterminate, so too is slog(A), where A is a fixed point of exponentiation.

I should preface this with the assumption that it also depends which branch we're in.

For example, consider the number 0.787605370443680 - 0.755132477752332*I. Note that this number is well within the radius of convergence for the power series derived by Andrew's slog at 0.

Exponentiate this three times, and you'll arrive at 0.318131505204764 + 1.33723570143069*I, which is A for base e.

So slog(A) is equal to 3+slog(0.787605370443680 - 0.755132477752332*I), in some branch of the slog. But in the principal branch, it's at the singularity, and hence the value is indeterminate.