Quadrature Formulas of Quasi-Interpolation Type for Singular Integrals with Hilbert Kernel Original Research Article

In this paper, we first establish quadrature formulas of trigonometric interpolation type for proper integrals of periodic functions with periodic weight, then we use the method of separation of singularities to derive those for corresponding singular integrals with Hilbert kernel. The trigonometric precision, the type, the estimate of the remainder, and the convergence of each quadrature formula derived here are also established.