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.