Mathematika

Research Article

NEW REPRESENTATIONS FOR APÉRY-LIKE SEQUENCES

Heng Huat Chana1a2 and Wadim Zudilina3

a1 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543

a2 Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany (email: matchh@nus.edu.sg)

a3 School of Mathematical and Physical Sciences, University of Newcastle, Callaghan NSW 2308, Australia (email: wadim.zudilin@newcastle.edu.au)

Abstract

We prove algebraic transformations for the generating series of three Apéry-like sequences. As application, we provide new binomial representations for the sequences. We also illustrate a method that derives three new series for 1/π from a classical Ramanujan’s series.

(Received April 08 2009)

MSC (2000)

  • 11F11;
  • 11F20 (primary);
  • 33C20 (secondary)