  Explicit exact formulas are presented, up to fourth order in a strict chiral
covariant derivative expansion, for the normal parity component of the
Euclidean effective action of even-dimensional Dirac fermions. The bosonic
background fields considered are scalar, pseudo-scalar, vector and axial
vector. No assumptions are made on the internal symmetry group and, in
particular, the scalar and pseudo-scalar fields need not be on the chiral
circle.
