The Riemann Boundary Value Problem in a Half-Plane for Generalized Analytic Functions with a Supersingular Line

We study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for one generalized Cauchy–Riemann equation with a strong coefficient singularity. To solve this problem, it is necessary to derive a structural formula for the general solution to the equation and conduct a complete study of the solvability of the Riemann boundary value problem for analytic function with an infinite power-order index. Based on this study, a general solution formula and a picture of the solvability of the boundary value problem for generalized analytic functions are derived.