Recurrence Relations for Meixner Multiple Orthogonal Polynomials on Interlacing Lattices

We consider the product of two classical Meixner weight functions whose arguments are shifted with respect to each other. Its restriction to the corresponding integer lattices generates a system of two discrete weights. Under certain conditions on the parameters, this system is perfect and has positive weights. Nevertheless, it is neither an Angelesco system nor a Nikishin system. The corresponding orthogonal polynomials are known to satisfy a four-term recurrence relation for the step-line indices. In this paper, we find explicit expressions for the coefficients of these relations. Passing to limits then yields the coefficients of four-term recurrence relations for a few other families.