Mathematical Notes

, Volume 101, Issue 5–6, pp 759–777 | Cite as

Finding the coefficients in the new representation of the solution of the Riemann–Hilbert problem using the Lauricella function

  • S. I. Bezrodnykh
Volume 101, Number 5, May, 2017


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.


Riemann–Hilbert problem with piecewise constant data Lauricella function FD(N) Jacobi-type formula Christoffel–Schwartz integral 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Federal Research Center “Computer Science and Control,”Russian Academy of SciencesMoscowRussia
  2. 2.RUDN UniversityMoscowRussia
  3. 3.Sternberg Astronomical InstituteLomonosov Moscow State UniversityMoscowRussia

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