Abstract: With the extension rule of the method of approximate values ot Dirac δ functiona set regularization equations for the electron self-energy is developed. The equations are similar to those in reference books such as the Pauli-Villars as well as the dimensional regularization equations. The renormalized self-energy equation for electrons is as well developed which is the same as that in reference books. Finally the counterterm Lagrangian equation is confirmed.

Key words: quantum field interactions, self-energy for fermions, ultra-violet divergence, Dirac δ function