  We discuss the ground state properties of a one-dimensional bosonic system
doped with an impurity (the so-called Bose polaron problem). We introduce a
formalism that allows us to calculate analytically the thermodynamic
zero-temperature properties of this system with weak and moderate boson-boson
interaction strengths for any boson-impurity interaction. Our approach is
validated by comparing to exact quantum Monte Carlo calculations. In addition,
we test the method in finite size systems using numerical results based upon
the similarity renormalization group. We argue that the introduced approach
provides a simple analytical tool for studies of strongly interacting impurity
problems in one dimension.
