Suppose you have a power series $S(-)$ in a quaternion $q$, and the coefficients in S are complex numbers, and the radius of convergence is $1.$ Then the boundary of the region of convergence is the unit $3-$sphere.
Question A: I am curious about whether the points of convergence of the series $S(z)$, with $z$ a complex number such that $|z|=1,$ generalize for $S(q)$ into interesting curves, or surfaces, or at least sets, on the unit 3-sphere.
Question B: Similar question for the sets of singular points, IF analytic continuation even makes sense for quaternions. Thanks.