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 and the remaining onecontains harmonic numbers of order . As conclusions, Sun's five conjectural series are proved.
Keywords
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