  This note supplements the work of Gomez-Ullate, Kamran and Milson on the
X_(1)-Jacobi polynomials which are orthogonal in a weighted Hilbert function
space on the the interval (-1,+1) of the real line. These polynomials are
generated by a second-order ordinary linear differential equation with a
spectral parameter. Some additional information on the Sturm-Liouville form of
this equation is given in this note, together with details of the singular
differential operators generated in the weighted Hilbert function space. In
particular, structured boundary conditions are given to determine the special
self-adjoint operator, whose discrete spectrum and associated eigenvectors
yield the X_(1)-Jacobi polynomials.
