05/08/2023, 03:53 AM
I know what I've described so far is just an algorithm. But this algorithm allows for the following graph of \(\text{tet}_K(z)\) (Kneser's tetration) from \(-2 \le \Re(z) \le 0\) and \(|\Im(z)| \le 1\). It screws up near \(\Im(z) = 1\) and will continue to do so as we increase the imaginary argument. But in this square, I can generate Kneser's taylor series at any point, and do so in pretty record time. It screws up on the top borders, but otherwise this is perfect.
The only thing I steal from Sheldon is the coefficients:
\[
\{a_j\}_{j=1}^\infty = \left\{\frac{d^j}{dz^j}\Big{|}_{z=1} \text{slog}_K(z)\right\}_{j=1}^\infty\\
\]
The only thing I steal from Sheldon is the coefficients:
\[
\{a_j\}_{j=1}^\infty = \left\{\frac{d^j}{dz^j}\Big{|}_{z=1} \text{slog}_K(z)\right\}_{j=1}^\infty\\
\]