Abstract
In this work, we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double Euler sums ζ(r‾,s), ζ(r,s‾) and ζ(r‾,s‾) with r+s odd in terms of zeta values. We also give a direct proof of a hypergeometric identity which is a limiting case of a basic hypergeometric identity of Andrews. Finally, we gave another proof for the formula of Zagier on the multiple zeta values ζ(2,…,2,3,2,…,2).
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