  We verify to order alpha_s^4 two previously conjectured relations, valid in
four dimensions, between constant terms in threshold resummation (for Deep
Inelastic Scattering and the Drell-Yan process) and the second logarithmic
derivative of the massless quark form factor. The same relations are checked to
all orders in the large beta_0 limit; as a byproduct a dispersive
representation of the form factor is obtained. These relations allow to compute
in a symmetrical way the three-loop resummation coefficients B_3 and D_3 in
terms of the three-loop contributions to the virtual diagonal splitting
function and to the quark form factor, confirming results obtained in the
literature.
