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Ramanujan-inspired series for $1/\pi$ involving harmonic numbers

Number Theory 2023-07-11 v4

Abstract

By applying the derivative operator to the known identities from hypergeometric series or WZ pairs, we obtain seven series associated with harmonic numbers. Specifically, six of them are Ramanujan-like formulas for 1/π1/\pi and the remaining onecontains harmonic numbers of order 22. As conclusions, Sun's five conjectural series are proved.

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Cite

@article{arxiv.2305.00498,
  title  = {Ramanujan-inspired series for $1/\pi$ involving harmonic numbers},
  author = {Qinghu Hou and Haihong He and Xiaoxia Wang},
  journal= {arXiv preprint arXiv:2305.00498},
  year   = {2023}
}

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11 pages