On the Numerical Evaluation of a Class of Finite‐Part Integrals

Two more methods for the derivation of the interpolatory quadrature rules (including Gaussian quadrature rules as a special case) for the numerical evaluation of finite-part integrals with a double-pole singularity inside the integration interval are presented. The first of these methods is based on the definition of finite-part integrals and the second of them on the second generalized PLEMELJ formula. The present results can be generalized to the case of finite-part integrals with pole singularities of higher order.