Asymptotics for Multiple Meixner Polynomials

Abstract

We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arvesú et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the equilibrium problem with constrain to describe their zero distribution. Then analyzing the limiting behavior of the coefficients of the recurrence relations for Multiple Meixner polynomials we obtain the main term of their asymptotics.

The n-root asymptotic behavior of multiple Meixner polynomials is studied. A method based on an algebraic function formulation in connection with some available techniques from logarithmic potential theory has been developed. It represents an alternative to the use of Riemann-Hilbert techniques and the steepest descent method for oscillatory RH problems, when dealing with multiple orthogonality