  We 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 we prove that the Jacobi type
polynomials always satisfy higher-order recurrence relations (i.e., they are
bispectral). We also prove that the Krall-Jacobi families are the only Jacobi
type polynomials which are orthogonal with respect to a measure on the real
line.
