Unlike what has been reported by Villalba and Pino ( J. Phys.: Condens. Matter 8 8067) the results of the shifted 1/N expansion method, obtained by Mustafa ( J. Phys.: Condens. Matter 5 1327), for the two-dimensional hydrogenic donor impurity states in an arbitrary magnetic field are accurate and fast converging. The exact analytical results at zero- and high-magnetic-field limits were reproduced in this paper by Mustafa and appeared to be in excellent agreement with those of Martin et al ( Phys. Rev. B 45 8359).