Abstract
Applying the multiplicate forms of Gould–Hsu inverse series relations to the Pfaff–Saalschütz summation theorem, we establish several infinite series expressions for \(\pi \) and \(1/\pi \), including three typical ones due to Ramanujan (Journal of Mathematics 45:350–372, 1914)
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In memory of my teacher Professor L. C. Hsu.
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Chu, W. Ramanujan-like formulae for \(\pi \) and \(1/\pi \) via Gould–Hsu inverse series relations. Ramanujan J 56, 1007–1027 (2021). https://doi.org/10.1007/s11139-020-00337-z
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DOI: https://doi.org/10.1007/s11139-020-00337-z
Keywords
- Classical hypergeometric series
- Pfaff–Saalschütz summation theorem
- Gould–Hsu inverse series relations
- Infinite series expression for \(\pi \)
- Ramanujan’s series for \(1/\pi \)