Bispectral Jacobi type polynomials (Q2078935)

The authors study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi type polynomials include, as particular cases, the Krall-Jacobi polynomials. As the main results the authors prove that the Jacobi type polynomials always satisfy higher-order recurrence relations (i.e., they are bispectral). This paper also provides a proof concerning that the Krall-Jacobi families are the only Jacobi type polynomials which are orthogonal with respect to a measure on the real line.