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WELL-POISED HYPERGEOMETRIC TRANSFORMATIONS OF EULER-TYPE MULTIPLE INTEGRALS

Published online by Cambridge University Press:  23 July 2004

W. ZUDILIN
Affiliation:
Department of Mechanics and Mathematics, Moscow Lomonosov State University, Vorobiovy Gory, GSP-2, 119992 Moscow, Russiawadim@ips.ras.ru
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Abstract

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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2004

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Footnotes

This work was supported by an Alexander von Humboldt research fellowship and partially supported by grant 03-01-00359 of the Russian Foundation for Basic Research.