Method for the Calculation of Abscissas and Weight Factors Using Gaussian Integration for Integrands with a Logarithmic Singularity

摘要

A method for the calculation of abscissas and weight factors using Gaussian integration for integrands with a logarithmic singularity is presented. The method shows good convergent properties and allows for the accurate estimation of the error. A program is supplied for the generation of orthogonal polynomials with weight Log(x) to order n, and numerical tables for the Gaussian integration method are provided. Keywords: Abscissas, Gaussian integration, Orthogonal polynomials.(JHD)