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Mat. Zametki, 2017, Volume 101, Issue 5, Pages 647–668 (Mi mz11530)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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 $F_D^{(N)}$. 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 $F_D^{(N)}$, 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.”


DOI: https://doi.org/10.4213/mzm11530

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English version:
Mathematical Notes, 2017, 101:5, 759–777

Bibliographic databases:

UDC: 517.5
Received: 02.11.2016

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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\by S.~I.~Bezrodnykh
\paper Finding the Coefficients in the New Representation of the Solution of the Riemann--Hilbert Problem Using the Lauricella Function
\jour Mat. Zametki
\yr 2017
\vol 101
\issue 5
\pages 647--668
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\crossref{https://doi.org/10.4213/mzm11530}
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\elib{http://elibrary.ru/item.asp?id=29106608}
\transl
\jour Math. Notes
\yr 2017
\vol 101
\issue 5
\pages 759--777
\crossref{https://doi.org/10.1134/S0001434617050029}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85021287719}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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