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Israel Journal of Mathematics

, Volume 194, Issue 1, pp 183–207 | Cite as

Legendre polynomials and Ramanujan-type series for 1/π

  • Heng Huat Chan
  • James Wan
  • Wadim Zudilin
Article

Abstract

We resolve a family of recently observed identities involving 1/π using the theory of modular forms and hypergeometric series. In particular, we resort to a formula of Brafman which relates a generating function of the Legendre polynomials to a product of two Gaussian hypergeometric functions. Using our methods, we also derive some new Ramanujan-type series.

Keywords

Modular Form Elliptic Function Legendre Polynomial Eisenstein Series Algebraic Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Department of MathematicsNational University of SingaporeSingaporeSingapore
  2. 2.School of Mathematical and Physical SciencesThe University of NewcastleCallaghanAustralia

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