The Riemann problem for functions with polar lines of higher orders

© 2014, Allerton Press, Inc. We consider solutions of the jump problem, homogeneous and inhomogeneous Riemann problems for functions with polar lines of orders pk +1 (k = 1, 2, … ), pk ⩾ 0. We study the cases of continuous and discontinuous coefficients. In the special case pk = 0 the obtained results turn into the earlier known ones