Two-dimensional low-energy scattering of a quantum particle in the summed field of Coulomb and power-law potentials

We study the two-dimensional scattering of a quantum particle by the force center acting on this particle via a superposition of a Coulomb potential and a power-law potential $V_0\,r^{-\beta}$ with the exponent $\beta\in (1,2)$. We find the explicit low-energy asymptotic forms of all partial phases and scattering amplitudes.