Constant terms in threshold resummation and the quark form factor

We verify to order alpha(4)(s) 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 by-product 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.