Orthogonality of the Jacobi polynomials with negative integer parameters

AbstractIt is well known that the Jacobi polynomials Pn(α,β)(x) are orthogonal with respect to a quasi-definite linear functional whenever α,β, and α+β+1 are not negative integer numbers. Recently, Sobolev orthogonality for these polynomials has been obtained for α a negative integer and β not a negative integer and also for the case α=β negative integer numbers.In this paper, we give a Sobolev orthogonality for the Jacobi polynomials in the remainder cases

Manuel Alfaro, a,1 Juan J. Moreno-Balca ´ zar, b,c,2 a,,1,a

Laguerre–Sobolev orthogonal polynomials: asymptotics for coherent pairs of type I