  Applications of a method recently suggested by one of the authors (R.L.) are
presented. This method is based on the use of dimensional recurrence relations
and analytic properties of Feynman integrals as functions of the parameter of
dimensional regularization, $d$. The method was used to obtain analytical
expressions for two missing constants in the $\epsilon$-expansion of the most
complicated master integrals contributing to the three-loop massless quark and
gluon form factors and thereby present the form factors in a completely
analytic form. To illustrate its power we present, at transcendentality weight
seven, the next order of the $\epsilon$-expansion of one of the corresponding
most complicated master integrals. As a further application, we present three
previously unknown terms of the expansion in $\epsilon$ of the three-loop
non-planar massless propagator diagram. Only multiple $\zeta$ values at integer
points are present in our result.
