ABSTRACT
Singular integrals are defined for unbounded integrands or over unbounded ranges of integration. These integrals do not exist as proper or improper Riemann integrals, but are defined as limits of certain proper integrals. The Gauss-Christoffel quadrature rule is discussed for singular integrals in general, and for those integrals that have singularities near and on the real axis. Product integration, endpoint and interior singularities and certain methods for acceleration of convergence are presented. Sidi’s quadrature rules are studied, and tables are provided for the nodes and weights of the Gauss-Christoffel and Sidi’s rules. Hypersingular integrals, specifically the Cauchy p.v. and the Hadamard finite-part integrals, are discussed.
