Note on the approximation of powers of the distance in two-dimensional domains

Although Newman's trick has been mainly applied to the approximation of uni variate functions, it is also appropriate for the approximation of multivar iate functions that are encountered in connection with Green's functions fo r elliptic differential equations. The asymptotics of the real-valued funct ion on a ball in 2-space coincides with that for an approximation problem i n the complex plane. The note contains an open problem.