Some Symmetry and Duality Theorems on Multiple Zeta(-Star) Values

Kwang-Wu Chen (), Minking Eie and Yao Lin Ong
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Kwang-Wu Chen: Department of Mathematics, University of Taipei, Taipei 100234, Taiwan
Minking Eie: Department of Mathematics, National Chung Cheng University, Chia-Yi 62145, Taiwan
Yao Lin Ong: Executive Master of Business Administration, Chang Jung Christian University, Tainan City 71101, Taiwan

Mathematics, 2024, vol. 12, issue 20, 1-13

Abstract: In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. We find that the summation ∑ a + b = r − 1 ( − 1 ) a ζ ★ ( a + 2 , { 2 } p − 1 ) ζ ★ ( { 1 } b + 1 , { 2 } q ) equals ζ ★ ( { 2 } p , { 1 } r , { 2 } q ) + ( − 1 ) r + 1 ζ ★ ( { 2 } q , r + 2 , { 2 } p − 1 ) . With the help of this equation and Zagier’s ζ ★ ( { 2 } p , 3 , { 2 } q ) formula, we can easily determine ζ ★ ( { 2 } p , 1 , { 2 } q ) and several interesting expressions.

Keywords: multiple zeta value; multiple zeta-star value; duality theorem; Yamamoto’s integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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