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Matematicheskie Zametki, 2010, Volume 87, Issue 2, Pages 217–232
DOI: https://doi.org/10.4213/mzm8589 (Mi mzm8589) 		 
This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (546 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm8589
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.
Received: 30.01.2009
Revised: 09.07.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 2, Pages 204–217
DOI: https://doi.org/10.1134/S000143461001027X
Bibliographic databases:
UDC: 517.53
Language: Russian
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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  • https://doi.org/10.4213/mzm8589
  • https://www.mathnet.ru/eng/mzm/v87/i2/p217
    • This publication is cited in the following 7 articles:
    1. V. N. Sorokin, “On Polynomials Defined by the Discrete Rodrigues Formula”, Math. Notes, 113:3 (2023), 420–433  mathnet  crossref  crossref  mathscinet
    2. V. N. Sorokin, “Multipoint Padé Approximation of the Psi Function”, Math. Notes, 110:4 (2021), 571–577  mathnet  crossref  crossref  isi  elib
    3. V. N. Sorokin, “Hermite-Padé approximants to the Weyl function and its derivative for discrete measures”, Sb. Math., 211:10 (2020), 1486–1502  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. N. Sorokin, “Multipoint Hermite–Padé approximants for three beta functions”, Trans. Moscow Math. Soc., 2018, 117–134  mathnet  crossref  elib
    5. 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
    6. 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
    7. 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
    Citing articles in Google Scholar: Russian citations, English citations
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