Abstract

Multidimensional generalizations of a q-beta integral of Nasrallah–Rahman and Barnes’ second lemma are evaluated. These are integral analogues of Jackson, Dougall, and the Pfaff–Saalschütz summation theorem for hypergeometric series. These integrals can also be written as group integrals over the special unitary group, the compact symplectic groups or conjugation invariant integrals over the corresponding Lie algebras.

MSC codes

  1. 33A15
  2. 33A30
  3. 33A65
  4. 33A75

Keywords

  1. multivariate beta integrals
  2. multivariate Mellin–Barnes integrals
  3. q-beta integrals
  4. the classical groups

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Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 525 - 551
ISSN (online): 1095-7154

History

Submitted: 6 August 1990
Accepted: 14 June 1991
Published online: 17 February 2012

MSC codes

  1. 33A15
  2. 33A30
  3. 33A65
  4. 33A75

Keywords

  1. multivariate beta integrals
  2. multivariate Mellin–Barnes integrals
  3. q-beta integrals
  4. the classical groups

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