Asymptotic estimation of Gaussian quadrature error for a nonsingular integral in potential theory (Q2781219)

By following the approach that is described by \textit{J. D. Donaldson} and \textit{D. Elliott} [SIAM J. Numer. Anal. 9, 573-602 (1972; Zbl 0264.65020)], the author considers the \(n\)-point Gauss-Jacobi approximation of nonsingular integrals of the form NEWLINE\[NEWLINE\int^1_{-1}\mu(t)\phi(t)\log(z-t)dt,NEWLINE\]NEWLINE with Jacobi weight \(\mu\) and polynomial \(\phi\). Among other things, he derives an estimate for the quadrature error that is asymptotic as \(n\to\infty\). In addition, he outlines the extension of the theory to similar integrals defined on more general arcs.