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On Some General Tornheim-Type Series

Author

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  • Kwang-Wu Chen

    (Department of Mathematics, University of Taipei, Taipei 100234, Taiwan)

Abstract

In this paper, we solve the open problem posed by Kuba by expressing ∑ j , k ≥ 1 H k ( u ) H j ( v ) H j + k ( w ) j r k s ( j + k ) t as a linear combination of multiple zeta values. These sums include Tornheim’s double series as a special case. Our approach is based on employing two distinct methods to evaluate the specific integral proposed by Yamamoto, which is associated with the two-poset Hasse diagram. We also provide a new evaluation formula for the general Mordell–Tornheim series and some similar types of double and triple series.

Suggested Citation

  • Kwang-Wu Chen, 2024. "On Some General Tornheim-Type Series," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1867-:d:1415334
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    References listed on IDEAS

    as
    1. Anthony Sofo & Amrik Singh Nimbran, 2019. "Euler Sums and Integral Connections," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
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    Cited by:

    1. Kwang-Wu Chen, 2024. "On General Alternating Tornheim-Type Double Series," Mathematics, MDPI, vol. 12(17), pages 1-30, August.

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