  We consider pionic hydrogen A_(pi p), the bound pi^- p state. Within the
quantum field theoretic and relativistic covariant approach we calculate the
shift and width of the energy level of the ground state of pionic hydrogen
caused by strong low-energy interactions treated perturbatively. The
generalization of the Deser-Goldberger-Baumann-Thirring (DGBT) formulas (Phys.
Rev. 96, 774 (1954)) is given. The generalized DGBT formulas for the energy
level displacement of the ground state of pionic hydrogen contain the
non-perturbative and model-independent correction about 1%, caused by the
relativistic covariant smearing of the wave function of the ground state around
origin. This non-perturbative correction is very important for the precise
extraction of the S-wave scattering lengths of pion-nucleon scattering from the
experimental data on the energy level displacements in pionic hydrogen by the
PSI Collaboration. In addition the shift of the energy level of the ground
state of pionic hydrogen is improved by the second order correction of strong
low-energy interactions which is about 0.1%. This testifies the applicability
of the perturbative treatment of strong low-energy interactions to the analysis
of pionic hydrogen. We show that the width of the energy level of the ground
state of pionic hydrogen is valid to all order of perturbation theory in strong
low-energy interactions.
