The full propagator (to fourth order) can be written (1 - Z)/(p^2 + Σ(p^2) - (1 - c) m^2)~~(1 - Z)/(p^2 - m^2) - (Σ(p^2) + c m^2)/(m^2 - p^2)^2. Thus the amplitude ff4 can be written (p^2 - m^2) (1 - Z) - Σ(p^2) - c m^2.

Series[(1 - a d)/((1 - b d) m^2 - p^2), {d, 0, 1}] // Simplify

1/(m^2 - p^2) + ((b m^2 + a (p^2 - m^2)) d)/(m^2 - p^2)^2 + O (d^2)

Converted by Mathematica  (July 10, 2003)