For AdS boundary conditions, we give a solution of the H₃⁺ two point function involving degenerate field with SL(2)-label b⁻²/2, which is defined on the full (u,z) unit square. It consists of two patches, one for z<u and one for u<z. Along the u = z "singularity", the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive b⁻²/2-shift equations for AdS₂ D-branes. We show that discrete as well as continuous AdS₂ branes are consistent with our novel shift equations without any new restrictions.