Abstract
We propose a Bethe-ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values iπ/(p+1), where p is a positive integer. All six boundary parameters are arbitrary, and need not satisfy any constraint. The solution is in terms of generalized T–Q equations, having more than one Q function. We find numerical evidence that this solution gives the complete set of 2N transfer matrix eigenvalues, where N is the number of spins.