This article is cited in 29 papers

On multiple orthogonal polynomials for discrete Meixner measures

V. N. Sorokin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves.
Bibliography: 9 titles.

Keywords: Meixner polynomials, Nikishin systems, Riemann surfaces and algebraic functions, logarithmic equilibrium potentials.

UDC: 517.53

MSC: 42C05

Received: 21.12.2009 and 12.04.2010

DOI: 10.4213/sm7672

 English version: Sbornik: Mathematics, 2010, 201:10, 1539–1561

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