Title: An elementary representation of the higher-order Jacobi-type differential equation,
Abstract: We investigate the differential equation for the Jacobi-type polynomials
which are orthogonal on the interval $[-1,1]$ with respect to the classical
Jacobi measure and an additional point mass at one endpoint. This scale of
higher-order equations was introduced by J. and R. Koekoek in 1999 essentially
by using special function methods. In this paper, a completely elementary
representation of the Jacobi-type differential operator of any even order is
given. This enables us to trace the orthogonality relation of the Jacobi-type
polynomials back to their differential equation. Moreover, we establish a new
factorization of the Jacobi-type operator which gives rise to a recurrence
relation with respect to the order of the equation.