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An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series. (English) Zbl 1114.33007
Summary: 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.

MSC:
33C20 Generalized hypergeometric series, \({}_pF_q\)
11J72 Irrationality; linear independence over a field
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