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An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series |
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| Authors: | C Krattenthaler T Rivoal |
| Institution: | 1. Institut Girard Desargues, Université Claude Bernard Lyon-I, 21, avenue Claude Bernard, F-69622, Villeurbanne, Cedex, France 2. Fakult?t für Mathematik, Universit?t Wien, Nordbergstra?e 15, A-1090, Vienna, Austria 3. Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, Université de Caen, BP 5186, 14032, Caen cedex, France 4. Institut Fourier, CNRS UMR 5582, Université Grenoble 1, 100 rue des Maths, BP 74, 38402, Saint-Martin d’Hères cedex, France |
| 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. Dedicated to Richard Askey on the occasion of his 70th birthday. Research partially supported by the programme “Improving the Human Research Potential” of the European Commission, grant HPRN-CT-2001-00272, “Algebraic Combinatorics in Europe”. 2000 Mathematics Subject Classification Primary—33C20; Secondary—11J72 |
| Keywords: | Riemann zeta function Hypergeometric series |
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