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

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.