The polynomial approximation behaviour of the class of functions $$F_s: {\bf R}^2 \backslash \{ (x_0, y_0) \} \to {\bf R}, \quad F_s(x,y) = ( (x-x_0)^2 + (y-y_0)^2 )^{-s},\quad s \in (0, \infty),$$ is studied in [Bra01]. There it is claimed that the obtained results can be embedded in a more general setting. This conjecture will be confirmed and complemented by a different approach than in [Bra01]. The key is to connect the approximation rate of Fs with its holomorphic continuability for which the classical Bernstein approximation theorem is linked with the convexity of best approximants. Approximation results of this kind also play a vital role in the numerical treatment of elliptic differential equations [Sau].