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Ramanujan–Sato series for $1/\pi $

Volume 207 / 2023

Tim Huber, Daniel Schultz, Dongxi Ye Acta Arithmetica 207 (2023), 121-160 MSC: Primary 11F03; Secondary 11F11. DOI: 10.4064/aa220621-19-12 Published online: 28 February 2023

Abstract

We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equations. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.

Authors

  • Tim HuberSchool of Mathematical and Statistical Sciences
    University of Texas Rio Grande Valley
    Edinburg, TX 78539, USA
    e-mail
  • Daniel SchultzDepartment of Mathematics
    Pennsylvania State University
    State College, PA 16802, USA
    e-mail
  • Dongxi YeSchool of Mathematics (Zhuhai)
    Sun Yat-sen University
    Zhuhai 519082, Guangdong, People’s Republic of China
    e-mail

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