The Hilbert Problem in a Half-plane for Generalized Analytic Functions with a Super-singular Point on the Contour of the Boundary Condition

In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index for one generalized Cauchy–Riemann equation with a supersingular point on the contour of the boundary condition. We obtain a structural formula for the general solution of this equation under constraints leading to an infinite index of the accompanying Hilbert boundary value problem for analytic functions. The solution of the latter problem is the basis for solving the boundary value problem for the generalized Cauchy–Riemann equation with a supersingular point.