This article is cited in 7 papers

Multipoint Hermite–Padé Approximations for Beta Functions

A. A. Kandayan^a, V. N. Sorokin<sup>b

a</sup> Federal Bureau of Insurance Supervision
^b M. V. Lomonosov Moscow State University

Abstract: We construct multipoint Hermite–Padé approximations for two beta functions generating the Nikishin system with infinite discrete measures and unbounded supports. The asymptotic behavior of the approximants is studied. The result is interpreted in terms of the vector equilibrium problem in logarithmic potential theory in the presence of an external field and constraints on measure.

Keywords: Hermite–Padé approximation, beta function, pole of a meromorphic function, logarithmic potential, Laurent series, Mittag–Leffler expansion, Cauchy transform, Riemann sphere, Rodrigues formula, Lebesgue measure.

UDC: 517.53

Received: 30.01.2009
Revised: 09.07.2009

DOI: 10.4213/mzm8589

 English version: Mathematical Notes, 2010, 87:2, 204–217

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