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For the dual pair considered, the Cauchy Harish-Chandra Integral, as a distribution on the Lie algebra, is the limit of the holomorphic extension of the reciprocal of the determinant. We compute that limit explicitly in terms of the Harish-Chandra orbital integrals.doi:10.2478/s11533-007-0023-3 fatcat:ufjlodxiibe5bfdlfnsga3vwny