Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae

Chu, Wenchang

doi:10.1090/S0025-5718-2011-02474-9

Dougall’s bilateral $_2H_2$-series and Ramanujan-like $\pi$-formulae
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Math. Comp. 80 (2011), 2223-2251 Request permission

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).

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