@Ansus
Thank you so much for finding that mistake! I fixed it in my original post.
Also, I noticed in the MathFacts page that it is a very complete overview, except for two things: the base-sqrt(2) tetration approximation: \( {}^{x}{(\sqrt{2})} \approx 2 \frac{x+1}{x+2} \), and intuitive/natural tetration, for which i would say that the matrix encoding of
which can be solved for \( \alpha(x) \) "intuitively" despite the fact that \( (C[b^x]^T - I) \) is a noninvertible matrix.
Thank you so much for finding that mistake! I fixed it in my original post.
Also, I noticed in the MathFacts page that it is a very complete overview, except for two things: the base-sqrt(2) tetration approximation: \( {}^{x}{(\sqrt{2})} \approx 2 \frac{x+1}{x+2} \), and intuitive/natural tetration, for which i would say that the matrix encoding of
\( \alpha(b^x) = \alpha(x) + 1 \)
is\( (C[b^x]^T - I)D[\alpha] = D[1] \)
which can be solved for \( \alpha(x) \) "intuitively" despite the fact that \( (C[b^x]^T - I) \) is a noninvertible matrix.
