The Riemann Boundary Value Problem for Generalized Analytical Functions with Supersingular Points on the Contour of the Boundary Condition

We investigate the Riemann boundary value problem with a boundary condition on the real axis for solutions of the generalized Cauchy–Riemann equation in a situation where the coefficient of the equation has \(n\) discontinuities of the second kind. We have obtained a formula for the general solution of the generalized Cauchy–Riemann equation. For limited solutions of this equation, we considered the Riemann boundary value problem with a finite index. We have reduced this Riemann boundary value problem to a similar problem for analytical functions with \(n\) points of vorticity and an infinite index. Based on these results, we have described the solvability of the Riemann problem for generalized analytical functions.