  In this note, we prove the uniqueness of the Neumann matrices of the
open-closed vertex in plane-wave light-cone string-field theory, first derived
for all values of the mass parameter mu in hep-th/0311231. We also prove the
existence and uniqueness of the inverse of an infinite dimensional matrix
necessary for the cubic vertex Neumann matrices, and give an explicit
expression for it in terms of mu-deformed Gamma functions. Methods of complex
analysis are used together with the analytic properties of the mu-deformed
Gamma functions. One of the implications of these results is that the
geometrical continuity conditions suffice to determine the bosonic part of the
vertices as in flat space.
