Coulomb scattering of a slow quantum particle in a space of arbitrary dimension

We assume that a charged quantum particle moves in a space of dimension $d=2,3,\dots$ and is scattered by a fixed Coulomb center. We derive and study expansions of the wave function and all radial functions of such a particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic approximations of the wave functions in the low-energy limit.