Separation of Variables in the open XXX chain

We apply the Sklyanin method of separation of variables to the reflection algebra underlying the open spin-1/2 XXX chain with non-diagonal boundary fields. The spectral problem can be formulated in terms of a TQ-equation which leads to the known Bethe equations for boundary parameters satisfying a constraint. For generic boundary parameters we study the asymptotic behaviour of the solutions of the TQ-equation.