References & Citations
Mathematics > Number Theory
Title: Ramanujan-inspired series for $1/π$ involving harmonic numbers
(Submitted on 30 Apr 2023 (v1), last revised 8 Jul 2023 (this version, 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 $1/\pi$ and the remaining onecontains harmonic numbers of order $2$. As conclusions, Sun's five conjectural series are proved.
Submission history
From: Haihong He [view email][v1] Sun, 30 Apr 2023 14:57:19 GMT (6kb)
[v2] Tue, 2 May 2023 11:18:25 GMT (6kb)
[v3] Thu, 11 May 2023 02:21:37 GMT (7kb)
[v4] Sat, 8 Jul 2023 11:06:44 GMT (9kb)
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