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.