Abstract
Multidimensional generalizations of beta type integrals of Bames, 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 G2 . 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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