Angle-resolved photoemission spectroscopy (ARPES) is used to study the spectral function of the optimally doped high- Tc superconductor (Bi,Pb) 2 Sr2 Ca Cu2 O8+δ in the vicinity of the antinodal point in the superconducting state. Using a parametrized self-energy function, it was possible to describe both the coherent and the incoherent spectral weight of the bonding and the antibonding band. The renormalization effects can be assigned to a very strong coupling to the magnetic resonance mode and at higher energies to a bandwidth renormalization by a factor of two, probably caused by a coupling to a continuum. The present reevaluation of the ARPES data allows one to come to a more reliable determination of the value of the coupling strength of the charge carriers to the mode. The experimental results for the dressing of the charge carriers are compared to theoretical models.