Ramanujan-inspired series for 1/π involving harmonic numbers

2023/04/30 by Hou, Qinghu, Haihong He, He, Haihong +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2305.00498

openalex publication_date 2023/04/30 · openalex created_date 2023/05/04 · openalex updated_date 2026/07/28

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/π and the remaining onecontains harmonic numbers of order 2. As conclusions, Sun's five conjectural series are proved.

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