Multiple-integral representations of very-well-poised hypergeometric series

Details Multiple-integral representations of very-well-poised hypergeometric series Multiple-integral representations of very-well-poised hypergeometric series

2002-06-18

arxiv.org/abs/math/0206177v1

Mathematics

Classical Analysis and ODEs

8 pages, AmSTeX; a 2-page summary to appear in Uspekhi Mat. Nauk [Russian Math. Surveys] 57:4 (2002)

Scientific paper

A new multiple-integral representation of a general family of very-well-poised hypergeometric series is proved. Inspite of an analytic character of the result, it is motivated by the recent arithmetic progress for the values of the Riemann zeta function at odd integers. The multiple integrals are of Euler-type and can be viewed as a natural generalization of Beukers' integrals for $\zeta(2)$ and $\zeta(3)$.

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