Abstract
A piecewise-continuous Riemann boundary problem with index plus-infinity on a closed rectifiable Jordan curve is studied; here the index of the problem takes into account the integral influence on its solvability of the argument and modulus of the coefficient of the problem and also the properties of the line of conjugation. One permits discontinuities of the second kind in the logarithm of the coefficient and the free term of the problem. The solution of the problem is constructed explicitly in the class of functions admitting a weak-power singularity.
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