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

  • Shaun Cooper
  • James G. Wan
  • Wadim Zudilin
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 221)

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.

Keywords

Apéry-like sequence Domb numbers Eisenstein series Holonomic function Modular form Modular parameterization Ramanujan’s series for \(1/\pi \) Sun’s conjectures Translation technique Zeilberger’s algorithm. 

2010 Mathematics Subject Classification

Primary 11Y60 33C20 Secondary 11B65 11F11 11Y55 65B10 

Notes

Acknowledgements

We thank the referee for helpful comments and suggestions.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Natural and Mathematical Sciences, Massey University — Albany, Private Bag 102904AucklandNew Zealand
  2. 2.Engineering Systems and Design, Singapore University of Technology and DesignSingaporeSingapore
  3. 3.School of Mathematical and Physical Sciences, The University of NewcastleCallaghan NSWAustralia

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