[en] An equation is derived defining the simplest possible S-sums < p,α/q,β>sub(kl) occurring in the second order Z-dependent theory of many-electron atoms. < l,α/l,β>sub(kl) are written in closed form for positive α,β and l integer >O; < p,α/q,β>sub(kl) for integer p>l,q>l can be reached by means of recurrence relations. The new method is demonstrated and tested on examples previously calculated in the literature. (author)