Andrew Robbins' Tetration Extension

[bo198214]

That:
\( \lim_{b \rightarrow 1} \text{slog}_b(z)_n = z^n - 1 \) (expanded about z=0) and:
\( \lim_{b \rightarrow \infty} \text{slog}_b(z)_n = -(1-z)^n \) (expanded about z=0),

Ah, ok. But you still assume that the coefficients of \( \text{slog}_b \) converge. I asked because it sounded in the beginning as if you had a proof for the convergence of the coefficients for base \( 1 \) and \( \infty \) which would be in itself somehow strange statement.