Asymptotics of Hermite–Padé approximants of the First Type for Discrete Meixner Measures.

Asymptotics of Hermite–Padé approximants of the first type for Weil functions of discrete Meixner measure and its derivative is studied. We describe a piecewise-analytic curve in the complex plane which attracts part of the zeros of the Meixner multiple orthogonal polynomials. This curve possesses a symmetry property in the equilibrium problem with an external field for logarithmic potential of vector measures with a constraint. Some connection between the considered Hermite–Padé approximants and the theory of Diophantine approximations is presented. [ABSTRACT FROM AUTHOR]