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On General Alternating Tornheim-Type Double Series

Author

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  • Kwang-Wu Chen

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

Abstract

In this paper, we express ∑ n , m ≥ 1 ε 1 n ε 2 m M n ( u ) M m ( v ) n r m s ( n + m ) t as a linear combination of alternating multiple zeta values, where ε i ∈ { 1 , − 1 } and M k ( u ) ∈ { H k ( u ) , H ¯ k ( u ) } , with H k ( u ) and H ¯ k ( u ) being harmonic and alternating harmonic numbers, respectively. These sums include Subbarao and Sitaramachandrarao’s alternating analogues of Tornheim’s double series as a special case. Our method is based on employing two different techniques to evaluate the specific integral associated with a 3-poset Hasse diagram.

Suggested Citation

  • Kwang-Wu Chen, 2024. "On General Alternating Tornheim-Type Double Series," Mathematics, MDPI, vol. 12(17), pages 1-30, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2621-:d:1463135
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    References listed on IDEAS

    as
    1. Kwang-Wu Chen, 2024. "On Some General Tornheim-Type Series," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    2. Anthony Sofo & Amrik Singh Nimbran, 2019. "Euler Sums and Integral Connections," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
    Full references (including those not matched with items on IDEAS)

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