I think it would have been worth mentioning! Analytics continuation always stays in the original manifold and thus doesn't extend into another dimension. It is true, though, that the local extension can lead to Riemann surfaces that can eventually "wrap around" and form "layers" that have multiple different value at the same original coordinate. This can be interpreted as pointing into another dimension (even though it is not doing so continuously (real-values)). I would guess there is a subset of methods for Hyperpolation that use this approach to hyperpolate some functions (maybe for functions for which analytical continuation isn't known yet).

The article gives a general but boring example: Extrusion. This is analogous to stepwise interpolation ($f\left(x\right)=f\left(x_i\right)$ such that $x_i\le x<x_{i+1}$), which is also boring. Depending on the constraints put on the function different methods result. For example, analytical functions can plausibly extended in the complex plane by choosing the simplest coefficients.

Hi Newbie, what are your thoughts on it?