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A high-order linear q-difference equation with polynomial coefficients having q-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation coincides with the number of orthogonality conditions that these polynomials satisfy. Some limiting situations when q -> 1 are studied. Indeed, the difference equation for Hahn multiple orthogonal polynomials given in Lee [J. Approx. Theory (2007), doi:10.1016/j.jat.2007.06.002] is obtained as a limiting case.
multiple orthogonal polynomials; hermite-pade approximation; difference equations; classical orthogonal polynomials of a discrete variable