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Cauchy Principal Value - an overview | ScienceDirect Topics Cauchy Principal Value Occasionally an isolated pole will be directly on the contour of an integration, causing the integral to diverge A simple example is provided by an attempt to evaluate the real integral
Definitions, properties and applications of finite-part integrals In particular in the next section we describe the concept and some main properties of Cauchy principal value integrals, since these are of importance in understanding finite-part integrals Indeed, they are fundamental ingredients for the definitions and properties of finite-part integrals, which we present in Section 3
Gaussian quadrature for certain two-dimensional hypersingular integrals The extrapolation method of Cauchy principal integrals by rectangle formula and other extrapolation methods of hypersingular integrals by Simpson formula are studied [16], [17] Numerical algorithms for two-dimensional and multi-dimensional singular integrals are also being developed [18], [19], [20], [21]