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We consider the open spin-s XXZ quantum spin chain with nondiagonal boundaryterms. By exploiting certain functional relations at roots of unity, we derivea generalized form of T-Q relation involving more than one independent Q(u),which we use to propose the Bethe-ansatz-type expressions for the eigenvaluesof the transfer matrix. At most two of the boundary parameters are set to bearbitrary and the bulk anisotropy parameter has values \eta = i\pi/2,i\pi/4,... We also provide numerical evidence for the completeness of theBethe-ansatz-type solutions derived, using s = 1 case as an example.

Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms