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Mathematics > Number Theory

Title: Ramanujan-inspired series for $1/π$ involving harmonic numbers

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.
Comments: 11 pages
Subjects: Number Theory (math.NT)
Cite as: arXiv:2305.00498 [math.NT]
  (or arXiv:2305.00498v4 [math.NT] for this version)

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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