Weighted sum formulas of multiple Hurwitz zeta functions

In this paper, we give weighted sum formulas of the multiple Hurwitz zeta functions \(\zeta (s_1, \ldots , s_n;a)\) $\zeta (s_1,\dots ,s_n;a)$ . As a corollary, we prove a well known explicit evaluation formula for \(\zeta (s, \ldots , s;a)\) $\zeta (s,\dots ,s;a)$ .