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Evaluating Infinite Series Involving Harmonic Numbers by Integration

Author

Listed:
  • Chunli Li

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhuokou 466001, China)

  • Wenchang Chu

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhuokou 466001, China)

Abstract

Eight infinite series involving harmonic-like numbers are coherently and systematically reviewed. They are evaluated in closed form exclusively by integration together with calculus and complex analysis. In particular, a mysterious series W is introduced and shown to be expressible in terms of the trilogarithm function. Several remarkable integral values and difficult infinite series identities are shown as consequences.

Suggested Citation

  • Chunli Li & Wenchang Chu, 2024. "Evaluating Infinite Series Involving Harmonic Numbers by Integration," Mathematics, MDPI, vol. 12(4), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:589-:d:1340068
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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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