In this paper we propose a quadrature method for the numerical solution of Cauchy singular integral
equations with additional fixed singularities. The unknown function is approximated by a weighted
polynomial which is the solution of a finite dimensional equation obtained discretizing the involved
integral operators by means of a Gauss-Jacobi quadrature rule. Stability and convergence results for the
proposed procedure are proved. Moreover, we prove that the linear systems one has to solve, in order to
determine the unknown coefficients of the approximate solutions, are well conditioned. The efficiency of
the proposed method is shown through some numerical examples
