Hilbert problem with unitary coefficient matrix

For the Hilbert problem with unitary matrix-valued coefficient function $G(t)$ a solution is obtained in the form of a series whose general term can be found by quadrature from $G(t)$. Sufficient conditions are determined for the convergence of this series, establishing the dependence of the rate of convergence on the “proximity” of $G(t)$ to the class of matrices of diagonal form, for which the Hilbert problem admits analytic solution in quadratures. The obtained solutions are used to construct the Jost matrix of the coupled $^3S_1+{^3D_1}$ partial channels of $np$ scattering.