This material has been published in Ramanujan J. 13 (2007), 203-219, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Academic Press. This material may not be copied or reposted without explicit permission.

Christian Krattenthaler and Tanguy Rivoal

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

(14 pages)

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.

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