Electron-phonon interaction and ınagne t ic field effects on a two-dimensional electran bound to a Coulomb center is st udied within the fraınework of a variational appıoxinıat ion consisting of an adiabatic polaronic wave function conected by a first ordeı peıt urbat ive extension by which it is possible to intenelate the strong and weak co upling co unte rpaıts of the co upled electron-phonon system. Vario us aspects of the problem is considered depeneling on the Coulomb interaction, magnetic field, and electron-phonon coupling st strength.