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

Christian Krattenthaler; Tanguy Rivoal

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

Classical Analysis and ODEs 2007-05-23 v2 Number Theory

Authors: Christian Krattenthaler , Tanguy Rivoal

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.

Keywords

andrews identity multiple integrals very-well-poised hypergeometric series zudilin theorem riemann zeta function basic hypergeometric identity

Cite

@article{arxiv.math/0312148,
  title  = {An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series},
  author = {Christian Krattenthaler and Tanguy Rivoal},
  journal= {arXiv preprint arXiv:math/0312148},
  year   = {2007}
}

Comments

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

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

Abstract

Keywords

Cite

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