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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kwang-Wu Chen & Minking Eie & Yao Lin Ong, 2024. "Some Symmetry and Duality Theorems on Multiple Zeta(-Star) Values," Mathematics, MDPI, vol. 12(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3292-:d:1502778
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    References listed on IDEAS

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    1. Xu, Ce, 2019. "Evaluations of nonlinear Euler sums of weight ten," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 594-611.
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