Israel Journal of Mathematics

, Volume 194, Issue 1, pp 183–207

Legendre polynomials and Ramanujan-type series for 1/π

Authors

    • Department of MathematicsNational University of Singapore
  • James Wan
    • School of Mathematical and Physical SciencesThe University of Newcastle
  • Wadim Zudilin
    • School of Mathematical and Physical SciencesThe University of Newcastle
Article

DOI: 10.1007/s11856-012-0081-5

Cite this article as:
Chan, H.H., Wan, J. & Zudilin, W. Isr. J. Math. (2013) 194: 183. doi:10.1007/s11856-012-0081-5

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.

Copyright information

© Hebrew University Magnes Press 2012