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

S. I. Bezrodnykh

Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 647-668.

Résumé

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.

Détail

Keywords: Riemann–Hilbert problem with piecewise constant data, Lauricella function $F_D^{(N)}$, Christoffel–Schwartz integral.
Mots-clés : Jacobi-type formula

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