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13 (2007), 203-219,
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Christian Krattenthaler and
An identity of Andrews, multiple integrals,
and very-well-poised hypergeometric series
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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