In a previous paper, we presented conjectures of the recurrence relations
with constant coefficients for the multi-indexed orthogonal polynomials of
Laguerre, Jacobi, Wilson and Askey-Wilson types. In this paper we present a
proof for the Laguerre and Jacobi cases. Their bispectral properties are also
discussed, which give a method to obtain the coefficients of the recurrence
relations explicitly. This paper extends to the Laguerre and Jacobi cases the
bispectral techniques recently introduced by G\'omez-Ullate et al. to derive
explicit expressions for the coefficients of the recurrence relations satisfied
by exceptional polynomials of Hermite type.Comment: 37 pages. Comments added, typo in (A.15) corrected, reference
information updated. To appear in J.Math.Phy
