Characterizations of Bochner-Krall orthogonal polynomials of Jacobi type

Abstract

Let {Pn(x)}(n=0)(infinity) be an orthogonal polynomial system relative to a compactly supported measure. We find characterizations for {P-n(x)}(n=0)(infinity) to be a Bochner-Krall orthogonal polynomial system, that is, {P-n(x)}(n=0)(infinity) are polynomial eigenfunctions of a linear differential operator of finite order. In particular, we show that {P-n(x)}(n=0)(infinity) must be generalized Jacobi polynomials which are orthogonal relative to a Jacobi weight plus two point masses.