  The one-dimensional optical polaron is treated on the basis of the
perturbation theory in the weak coupling limit. A special matrix diagrammatic
technique is developed. It is shown how to evaluate all terms of the
perturbation theory for the ground-state energy of a polaron to any order by
means of this technique. The ground-state energy is calculated up to the eighth
order of the perturbation theory. The effective mass of an electron is obtained
up to the sixth order of the perturbation theory. The radius of convergence of
the obtained series is estimated. The obtained results are compared with the
results from the Feynman polaron theory.
