Infinite series about harmonic numbers	inspired by Ramanujan–like formulae

Chunli Li; Wenchang Chu; Chunli Li; Wenchang Chu

doi:10.3934/era.2023236

Electronic Research Archive

2023, Volume 31, Issue 8: 4611-4636. doi: 10.3934/era.2023236

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Research article

Infinite series about harmonic numbers inspired by Ramanujan–like formulae

Chunli Li ,
Wenchang Chu ^,

School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), China

Received: 08 March 2023 Revised: 17 June 2023 Accepted: 20 June 2023 Published: 28 June 2023

By employing the coefficient extraction method from hypergeometric series, we shall establish numerous closed form evaluations for infinite series containing central binomial coefficients and harmonic numbers, including several conjectured ones made by Z.-W. Sun.
- harmonic number,
- central binomial coefficient,
- hypergeometric series
Citation: Chunli Li, Wenchang Chu. Infinite series about harmonic numbersinspired by Ramanujan–like formulae[J]. Electronic Research Archive, 2023, 31(8): 4611-4636. doi: 10.3934/era.2023236

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Abstract

By employing the coefficient extraction method from hypergeometric series, we shall establish numerous closed form evaluations for infinite series containing central binomial coefficients and harmonic numbers, including several conjectured ones made by Z.-W. Sun.

References

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