Explicit Formulas for the Scalar Modes in Seiberg-Witten Theory with an Application to the Argyres-Douglas Point

General formulas for the scalar modes a_i and a^i_D in the Seiberg-Witten SU(N) setting are derived in the cases with and without massive hypermultiplets. Subsequently these formulas are applied in a study of the SU(3) Argyres-Douglas point. We use this example to study the question, whether the scalar modes admit an interpretation in terms of BPS mass states everywhere in moduli space. The paper collects, in an appendix, various facts on the function Lauricella F_D^(n), which naturally appears in the derived formulas.