Holonomic Alchemy and Series for \(1/\pi \)
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.
KeywordsApéry-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 ClassificationPrimary 11Y60 33C20 Secondary 11B65 11F11 11Y55 65B10
We thank the referee for helpful comments and suggestions.
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