Gauss-Chebyshev quadrature formulae for strongly singular integrals

Abstract

This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard’s finite-part sense. The quadrature formulae are derived from those for Cauchy singular integrals.