On multiple orthogonal polynomials for three Meixner measures

Abstract

Multiple orthogonal polynomials for three discrete Meixner measures with identical exponential decay at infinity are studied. These polynomials are the denominators of the type II Hermite–Padé approximants to some hypergeometric functions. The limit distribution of zeros of such polynomials scaled in a certain way is described in terms of equilibrium logarithmic potentials and in terms of algebraic curves.