This article is cited in 8 papers

Multipoint Padé Approximations of the Beta Function

A. A. Kandayan

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

Abstract: We study multipoint rational approximations with free poles for the beta function. The denominators of the approximations satisfy orthogonality relations with variable weight with respect to a discrete measure. We obtain the limit distribution of zeros of the denominators. A potential-theoretic interpretation of the results obtained is given.

Keywords: beta function, Padé approximation, logarithmic potential theory, Rakhmanov's equilibrium problem, Rodrigues' formula, Cauchy transform.

UDC: 517.51

Received: 22.10.2007
Revised: 23.01.2008

DOI: 10.4213/mzm4122

 English version: Mathematical Notes, 2009, 85:2, 176–189

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