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Matematicheskie Zametki, 2017, Volume 101, Issue 5, Pages 647–668
DOI: https://doi.org/10.4213/mzm11530 (Mi mzm11530) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Finding the Coefficients in the New Representation of the Solution of the Riemann–Hilbert Problem Using the Lauricella Function

S. I. Bezrodnykhabc

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
b Peoples Friendship University of Russia, Moscow
c Lomonosov Moscow State University, P. K. Sternberg Astronomical Institute
Full-text PDF (706 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm11530
Abstract: The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F(N)D. The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids.
Keywords: Riemann–Hilbert problem with piecewise constant data, Lauricella function F(N)D, Jacobi-type formula, Christoffel–Schwartz integral.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00781
16-07-01195
Ministry of Education and Science of the Russian Federation 5-100
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the Ministry of Education and Science of the Russian Federation on the “Program 5-100 to Improve the Competitiveness of RUDN University among the World's Leading Research and Educational Centers in 2016–2020,” by the Russian Foundation for Basic Research under grants 16-01-00781 and 16-07-01195, and by the RAN program “Modern Problems of Theoretical Mathematics” under project “Optimal Algorithms for the Solution of Problems of Mathematical Physics.”
Received: 02.11.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 5, Pages 759–777
DOI: https://doi.org/10.1134/S0001434617050029
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. I. Bezrodnykh, “Finding the Coefficients in the New Representation of the Solution of the Riemann–Hilbert Problem Using the Lauricella Function”, Mat. Zametki, 101:5 (2017), 647–668; Math. Notes, 101:5 (2017), 759–777
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm11530
  • https://doi.org/10.4213/mzm11530
  • https://www.mathnet.ru/eng/mzm/v101/i5/p647
    • This publication is cited in the following 3 articles:
    1. A. S. Demidov, Equations of Mathematical Physics, 2023, 91  crossref
    2. S. I. Bezrodnykh, V. I. Vlasov, “Asymptotics of the Riemann–Hilbert problem for a magnetic reconnection model in plasma”, Comput. Math. Math. Phys., 60:11 (2020), 1839–1854  mathnet  crossref  crossref  isi  elib
    3. S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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