Some 𝑞-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras

Gustafson, Robert A.

doi:10.1090/S0002-9947-1994-1139492-3

Some $q$-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras
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Trans. Amer. Math. Soc. 341 (1994), 69-119 Request permission

Abstract:

Multidimensional generalizations of beta type integrals of Barnes, Ramanujan, Askey-Wilson, and others are evaluated. These integrals are analogues of the summation theorems for multilateral hypergeometric series associated to the simple Lie algebras of classical type and type ${G_2}$. Many of these integrals can also be written as group integrals over a compact Lie group or conjugation invariant integrals over the corresponding Lie algebra.

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An

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