Proof of a rational Ramanujan-type series for \(1/ \pi\). The fastest one in level 3. (English) Zbl 07924573
Andrews, George E. (ed.) et al., Analytic and combinatorial number theory: the legacy of Ramanujan. Contributions in honor of Bruce C. Berndt. Selected papers based on the presentations at the conference, Champaign, IL, USA, June 6–9, 2019. Singapore: World Scientific. Monogr. Number Theory 12, 261-265 (2024).
Summary: Using a modular equation of level 3 and degree 23 due to Chan and Liaw, we prove the fastest known (conjectured to be the fastest one) convergent rational Ramanujan-type series for \(1/ \pi\) of level 3.
For the entire collection see [Zbl 07852528].
For the entire collection see [Zbl 07852528].
MSC:
| 33E05 | Elliptic functions and integrals |
| 33C05 | Classical hypergeometric functions, \({}_2F_1\) |
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
| 11F03 | Modular and automorphic functions |
