The *self-root* function is a simple function related to tetration.
It is the inverse function of the infinite tetrate, and thus
it corresponds to the infinite super-root.

Since `x`^{1/x} is such a simple function, we can expand it directly
using the series expansion of the exponential function:

The direct function gives the exponential coefficients (1, 1, -2, 3, 4, -90, 786, ...) or (Ax)

If we were to substitute `x` with *e*^{x} expanding about 0 gives the exponential coefficients (1, 1, -1, -2, 9, -4, -95, 414, ...) or (Ax).