Some identities for multiple Hurwitz zeta values

For any positive integers k,m,n with m≥2 and k≤n, let T(m,n,k) be the sum of all the multiple Hurwitz zeta valuesζ(s1,s2,…,sk;−12,−12,…,−12) of weight mn and depth k with arguments being multiples of m, i.e.,T(m,n,k)=∑s1+s2+…+sk=nsj∈Nζ(ms1,ms2,…,msk;−12,−12,…,−12). In this note, we obtain the evaluationT(m,n,k)=∑a+b=na,b∈N0(−1)a−k(ak)⋅ζ({m;−12}a)=⋅ζ⋆({m;−12}b), where ζ({m;−12}a) and ζ⋆({m;−12}b) denote the multiple Hurwitz zeta values and multiple Hurwitz zeta-star values respectively. Moreover, we give the evaluations of ζ({m;−12}n) and ζ⋆({m;−12}n) when m is even.