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Sum Formula of Multiple Hurwitz-Zeta Values
Let s_1,...,s_d be d positive integers and consider the multiple Hurwitz-zeta
value zeta(s_1,...,s_d;-1/2,...,-1/2)/2^w where w=s_1+...+s_d is called the
weight. For d<n+1, let T(2n,d) be the sum of all these values with even
arguments whose weight is 2n and whose depth is d. Recently Shen and Cai gave
formulas for T(2n,d) for d<6 in terms of t(2n), t(2)t(2n-2) and t(4)t(2n-4). In
this short note we generalize Shen-Cai's results to arbitrary depth by using
the theory of symmetric functions established by Hoffman.Comment: 7 page
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