  We explore manifestations of electron-phonon coupling on the electron
spectral function for two phonon modes in the cuprates exhibiting strong
renormalizations with temperature and doping. Applying simple symmetry
considerations and kinematic constraints, we find that the out-of-plane,
out-of-phase O buckling mode (B_1g) involves small momentum transfers and
couples strongly to electronic states near the anti-node while the in-plane
Cu-O breathing modes involve large momentum transfers and couples strongly to
nodal electronic states. Band renormalization effects are found to be strongest
in the superconducting state near the anti-node, in full agreement with
angle-resolved photoemission spectroscopy (ARPES) data.
