Holonomic alchemy and series for \(1/\pi \). (English) Zbl 1391.11165

Cooper, Shaun; Wan, James G.; Zudilin, Wadim

Andrews, George E. (ed.) et al., Analytic number theory, modular forms and \(q\)-hypergeometric series. In honor of Krishna Alladi’s 60th birthday, University of Florida, Gainesville, FL, USA, March 17–21, 2016. Cham: Springer (ISBN 978-3-319-68375-1/hbk; 978-3-319-68376-8/ebook). Springer Proceedings in Mathematics & Statistics 221, 179-205 (2017).

Summary: 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.
For the entire collection see [Zbl 1388.11003].

MSC:

11Y60	Evaluation of number-theoretic constants
11F11	Holomorphic modular forms of integral weight
11B65	Binomial coefficients; factorials; \(q\)-identities

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