## Dougall’s bilateral $_2H_2$-series and Ramanujan-like $\pi$-formulae

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## Abstract:

The modified Abel lemma on summation by parts is employed to investigate the partial sum of Dougall’s bilateral $_2H_2$-series. Several unusual transformations into fast convergent series are established. They lead surprisingly to numerous infinite series expressions for $\pi$, including several formulae discovered by Ramanujan (1914) and recently by Guillera (2008).## References

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## Additional Information

**Wenchang Chu**- Affiliation: Hangzhou Normal University, Institute of Combinatorial Mathematics, Hangzhou 310036, People’s Republic of China
- Address at time of publication: Dipartimento di Matematica, Università del Salento, Lecce–Arnesano, P. O. Box 193, Lecce 73100 Italy
- MR Author ID: 213991
- Email: chu.wenchang@unisalento.it
- Received by editor(s): May 13, 2010
- Received by editor(s) in revised form: July 31, 2010
- Published electronically: March 2, 2011
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**80**(2011), 2223-2251 - MSC (2010): Primary 33C20; Secondary 40A25, 65B10
- DOI: https://doi.org/10.1090/S0025-5718-2011-02474-9
- MathSciNet review: 2813357