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

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

2003-12-08

arxiv.org/abs/math/0312148v2

Ramanujan J. 13 (2007), 203-219.

Mathematics

Classical Analysis and ODEs

14 pages; AmS-LaTeX; several corrections, and a reference added

Scientific paper

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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