Generalized Gegenbauer orthogonal polynomials (Q5946593)

The aim of the author is to give a characterization of the so-called generalized Gegenbauer polynomials. He first shows the link between this functions and the classical Jacobi polynomials. Then he establishes both a differential-difference and a second order differential equation satisfied by these generalized polynomials. Finally, he introduces the so-called associated orthogonal polynomials and derives a fourth-order differential equation which is satisfied by all of them regardless their orders.