Research Article
Ramanujan-inspired series for 1/π involving harmonic numbers
https://doi.org/10.21203/rs.3.rs-3128120/v1
This work is licensed under a CC BY 4.0 License
published 09 Mar, 2024
Read the published version in Journal of Difference Equations and Applications →
posted
You are reading this latest preprint version
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 one contains harmonic numbers of order 2. As conclusions, Sun's five conjectural series are proved.
2010 Mathematics Subject Classification. Primary 33D15; Secondary 05A15.
Ramanujan-like formulas
harmonic numbers
the derivative operator
Dougal- l's well-poised 5F4-series
hypergeometric transformations
No competing interests reported.
published 09 Mar, 2024
Read the published version in Journal of Difference Equations and Applications →
posted
You are reading this latest preprint version