Crouching AGM, hidden modularity. (English) Zbl 1437.11058

Cooper, Shaun; Guillera, Jesús; Straub, Armin; Zudilin, Wadim

Nashed, M. Zuhair (ed.) et al., Frontiers in orthogonal polynomials and \(q\)-series. Papers based on the international conference, University of Central Florida, Orlando, FL, USA, May 10–12, 2015. Dedicated to Professor Mourad Ismail on his 70th birthday. Hackensack, NJ: World Scientific. Contemp. Math. Appl., Monogr. Expo. Lect. Notes 1, 169-187 (2018).

MSC:

11F11	Holomorphic modular forms of integral weight
33C20	Generalized hypergeometric series, \({}_pF_q\)
33F05	Numerical approximation and evaluation of special functions
65Q30	Numerical aspects of recurrence relations

Keywords:

modular form; arithmetic hypergeometric series; supercongruence; identity for \(1/\pi\); AGM iteration