  We present closed analytic expressions for the order $\alpha_s^2$ triangle
diagram contributions to the matrix elements of the singlet and non-singlet
axial vector currents between the vacuum and a quark-antiquark state. We have
calculated these vertex functions for arbitrary momentum transfer and for four
different sets of internal and external quark masses. We show that both the
singlet and non-singlet vertex functions satisfy the correct chiral Ward
identities. Using the exact expressions for the finite axial vector form
factors, we check the quality and the convergence of expansions at production
threshold and for asymptotic energies.
