  For a long time it has been a challenging goal to identify all orthogonal
polynomial systems that occur as eigenfunctions of a linear differential
equation. One of the widest classes of such eigenfunctions known so far, is
given by Koornwinder's generalized Jacobi polynomials with four parameters
$\alpha,\beta\in\mathbb{N}_{0}$ and $M,N \ge 0$ determining the orthogonality
measure on the interval $-1 \le x \le 1$. The corresponding differential
equation of order $2\alpha+2\beta+6$ is presented here as a linear combination
of four elementary components which make the corresponding differential
operator widely accessible for applications. In particular, we show that this
operator is symmetric with respect to the underlying scalar product and thus
verify the orthogonality of the eigenfunctions.
