  The abstract theory of boundary triples is applied to the classical Jacobi
differential operator and its powers in order to obtain the Weyl $m$-function
for several self-adjoint extensions with interesting boundary conditions:
separated, periodic and those that yield the Friedrichs extension. These
matrix-valued Nevanlinna--Herglotz $m$-functions are, to the best knowledge of
the author, the first explicit examples to stem from singular higher-order
differential equations.
  The creation of the boundary triples involves taking pieces, determined in a
previous paper, of the principal and non-principal solutions of the
differential equation and putting them into the sesquilinear form to yield maps
from the maximal domain to the boundary space. These maps act like
quasi-derivatives, which are usually not well-defined for all functions in the
maximal domain of singular expressions. However, well-defined regularizations
of quasi-derivatives are produced by putting the pieces of the non-principal
solutions through a modified Gram--Schmidt process.
