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Journal of the London Mathematical Society 2004 70(1):215-230; doi:10.1112/S0024610704005472
© 2004 by London Mathematical Society
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© The London Mathematical Society

Well-Poised Hypergeometric Transformations of Euler-Type Multiple Integrals

W. Zudilin

Department of Mechanics and Mathematics, Moscow Lomonosov State University Vorobiovy Gory, GSP-2, 119992 Moscow, Russia, wadim{at}ips.ras.ru

Received 15 April 2003. Revision received 15 November 2003.

Several new multiple-integral representations are proved for well-poised hypergeometric series and integrals. The results yield, in particular, transformations of the multiple integrals that cannot be achieved by evident changes of variable. All this generalizes some classical results of Whipple and Bailey in analysis and, on the other hand, certain analytic constructions with known connection to irrationality proofs for values of Riemann's zeta function at positive integers.


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