The Ramanujan Journal

, Volume 13, Issue 1–3, pp 203–219 | Cite as

An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series

Article

Abstract

We give a new proof of a theorem of Zudilin that equates a very-well-poised hypergeometric series and a particular multiple integral. This integral generalizes integrals of Vasilenko and Vasilyev which were proposed as tools in the study of the arithmetic behaviour of values of the Riemann zeta function at integers. Our proof is based on limiting cases of a basic hypergeometric identity of Andrews.

Keywords

Riemann zeta function Hypergeometric series 

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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Institut Girard DesarguesUniversité Claude Bernard Lyon-IVilleurbanneFrance
  2. 2.Fakultät für MathematikUniversität WienViennaAustria
  3. 3.Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139Université de Caen, BP 5186Caen cedexFrance
  4. 4.Institut Fourier, CNRS UMR 5582Université Grenoble 1Saint-Martin d’Hères cedexFrance

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