A generalization of Selberg’s beta integral
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We evaluate several infinite families of multidimensional integrals which are generalizations or analogs of Euler’s classical beta integral. We first evaluate a q-analog of Selberg’s beta integral. This integral is then used to prove the Macdonald-Morris conjectures for the affine root systems of types S(Cl) and S(Cl)Vand to give a new proof of these conjectures for S(BCl), S(Bl), S(Bl)Vand S(Dl). © 1990 American Mathematical Society.
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