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arXiv · 2305.00498

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

Qinghu Hou·Haihong He·Xiaoxia Wang
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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 $1/\pi$ and the remaining onecontains harmonic numbers of order $2$. As conclusions, Sun's five conjectural series are proved.

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Qinghu Hou, Haihong He, Xiaoxia Wang. 2023-04-30. Ramanujan-inspired series for $1/\pi$ involving harmonic numbers. https://arxiv.org/abs/2305.00498

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