  We present a new group-theoretical technique to calculate weak field
expansions for some Feynman diagrams using invariant polynomials of the
dihedral group. In particular we show results obtained for the first
coefficients of the three loop effective lagrangian of 1+1 QED in an external
constant field, where the dihedral symmetry appears. Our results suggest that a
closed form involving rational numbers and the Riemann zeta function might
exist for these coefficients.
