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Holonomic Alchemy and Series for \(1/\pi \)

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Analytic Number Theory, Modular Forms and q-Hypergeometric Series (ALLADI60 2016)

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Abstract

We adopt the “translation” as well as other techniques to express several identities conjectured by Z.-W. Sun by means of known formulas for \(1/\pi \) involving Domb and other Apéry-like sequences.

To Krishna Alladi,

on his smooth transition from the sixth decade

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Notes

  1. 1.

    The entry 4 / 196 in [8, Table 1] is a misprint and should be 1 / 196.

  2. 2.

    Multiply the argument of \(P_k\) in each of the Conjectures (6.8)–(6.13) in [19] by 4, and then take the reciprocal to get the values of x in the data.

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Acknowledgements

We thank the referee for helpful comments and suggestions.

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Correspondence to Shaun Cooper .

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Cooper, S., Wan, J.G., Zudilin, W. (2017). Holonomic Alchemy and Series for \(1/\pi \) . In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_12

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