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Mat. Zametki, 2010, Volume 87, Issue 2, Pages 217–232 (Mi mz8589)  

This article is cited in 3 scientific papers (total in 3 papers)

Multipoint Hermite–Padé Approximations for Beta Functions

A. A. Kandayana, V. N. Sorokinb

a 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

DOI: https://doi.org/10.4213/mzm8589

Full text: PDF file (546 kB)
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English version:
Mathematical Notes, 2010, 87:2, 204–217

Bibliographic databases:

UDC: 517.53
Received: 30.01.2009
Revised: 09.07.2009

Citation: A. A. Kandayan, V. N. Sorokin, “Multipoint Hermite–Padé Approximations for Beta Functions”, Mat. Zametki, 87:2 (2010), 217–232; Math. Notes, 87:2 (2010), 204–217

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Sorokin, “On multiple orthogonal polynomials for discrete Meixner measures”, Sb. Math., 201:10 (2010), 1539–1561  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. A. Kandayan, V. N. Sorokin, “Asymptotics of Multipoint Hermite–Padé Approximants of the First Type for Two Beta Functions”, Math. Notes, 101:6 (2017), 984–993  mathnet  crossref  crossref  mathscinet  isi  elib
    3. T. Rivoal, “Values of the Beta Function: from Ramanujan's Continued Fraction to Hermite–Padé Approximants”, Proc. Steklov Inst. Math., 298, suppl. 1 (2017), 57–69  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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