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NEW REPRESENTATIONS FOR APÉRY-LIKE SEQUENCES

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  10 December 2009

Heng Huat Chan  and
Wadim Zudilin
Heng Huat Chan
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543 Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany (email: matchh@nus.edu.sg)
Wadim Zudilin
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan NSW 2308, Australia (email: wadim.zudilin@newcastle.edu.au)

Abstract

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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.

MSC classification

Secondary: 11F11: Holomorphic modular forms of integral weight 11F20: Dedekind eta function, Dedekind sums 33C20: Generalized hypergeometric series, $_pF_q$

Information

Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 107 - 117
Copyright
Copyright © University College London 2010

References

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