This article is cited in 11 papers

Generalized Pollaczek polynomials

V. N. Sorokin

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

Abstract: For multiple orthogonal polynomials with respect to two Pollaczek weight functions weak asymptotics are obtained. It is shown that a solution of a vector equilibrium problem of the theory of logarithmic potential in the presence of an external field and with restriction imposed on the measures is given by the limit measure of the distribution of zeros.
Bibliography: 17 titles.

Keywords: Pollaczek polynomials, multiple orthogonal polynomials, vector equilibrium problem.

UDC: 517.53

MSC: 42C05

Received: 29.09.2008 and 26.01.2009

DOI: 10.4213/sm7446

 English version: Sbornik: Mathematics, 2009, 200:4, 577–595

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