Bethe ansatz derived from the functional relations of the openXXZchain for new special cases

The transfer matrix of the general integrable open XXZ quantum spin chain obeys certain functional relations at roots of unity. By exploiting these functional relations, we determine the Bethe ansatz solution for the transfer matrix eigenvalues for the special cases where all but one of the boundary parameters are zero, and the bulk anisotropy parameter is iπ/3, iπ/5, ....