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Well‐Poised Hypergeometric Transformations of Euler‐Type Multiple Integrals
Author(s) -
Zudilin W.
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005472
Subject(s) - type (biology) , hypergeometric function , euler's formula , mathematics , hypergeometric distribution , pure mathematics , mathematical analysis , geology , paleontology
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.