Summary: | 碩士 === 國立中正大學 === 數學系研究所 === 107 === Multiple zeta values and multiple zeta-star values are dened as
ζ(α_1,α_2,…,α_r)=∑_(1≤k1<k2<___<kr)▒〖k_1^(-α1) k_2^(-α2)… k_r^(-αr) 〗
and
ζ^* (α_1,α_2,…,α_r)=∑_(1≤k1≤k2≤___≤kr)▒〖k_1^(-α1) k_2^(-α2)… k_r^(-αr) 〗
for an r-tuple of positive integers (α_1,α_2,…,α_r) and α_r ≥ 2. For convenience,
we let α^k be the k repetitions of a.
In this thesis, we evaluate ζ^* ({2}^a,3, {2}^b) with α≥1 through re
ection
formulas. By considering Euler sums with two branches H1(α;β ) and H2(α;β)
and their duality relations we obtain
ζ^* ({2}^(b+1),1,{2}^a )+ζ^* ({2}^a,3,{2}^b )= ζ^* ({2}^(b+1) ) ζ^* (1,{2}^a ).
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