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We study the scalar product S_{l,m} between an on-shell and an off-shellBethe state in models with SU(3)-invariance, where l and m denote thecardinalities of the two sets of Bethe roots. We construct recursion relationsrelating S_{l,m} to scalar products of smaller dimension, namely S_{l-1,m} andS_{l,m-1}. Solving these recursion relations we obtain new multiple integralexpressions for S_{l,m}, whose integrands are (l+m) \times (l+m) determinants,and closely related to the Slavnov determinant expression for the SU(2) scalarproduct.

Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models