CARMA ANALYSIS AND NUMBER THEORY SEMINAR Speaker: Dr James Wan, Singapore University of Technology and Design Title: Legendre polynomials and Ramanujan-type series for $1/\pi$ Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 3:30 pm, Tue, 10th May 2011 Abstract: We resolve some recent and fascinating conjectural formulae for $1/\pi$ involving the Legendre polynomials. Our mains tools are hypergeometric series and modular forms, though no prior knowledge of modular forms is required for this talk. Using these we are able to prove some general results regarding generating functions of Legendre polynomials and draw some unexpected number theoretic connections. This is joint work with Heng Huat Chan and Wadim Zudilin. The authors dedicate this paper to Jon Borwein's 60th birthday. [Permanent link]