Israel Journal of Mathematics

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

Legendre polynomials and Ramanujan-type series for 1/π

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.

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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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