An alternative proof of a theorem of Zagier

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• 作者：Kh. Hessami Pilehrood ^{hessamik@gmail.com} ; T. Hessami Pilehrood ; ^{hessamit@gmail.com}
• 关键词：Multiple zeta value ; Multiple zeta star value ; Very-well-poised hypergeometric series ; Residue theorem ; Euler sum ; Digamma function
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：168-175
• 全文大小：272 K
• 卷排序：449

文摘

We give a new proof of Zagier's theorem on evaluation of multiple zeta (star) values at ({2}a,3,{2}b)({2}a,3,{2}b). The novelty of the proof consists in employing a hypergeometric identity of Andrews, which expresses a very-well-poised hypergeometric series in terms of a multiple series, and the residue theorem.