Asymptotic Gauss--Jacobi quadrature error estimation for Schwarz--Christoffel integrals
Journal of Approximation Theory
Gauss-Legendre quadrature for the evaluation of integrals involving the Hankel function
Journal of Computational and Applied Mathematics
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This paper considers the n-point Gauss-Jacobi approximation of nonsingular integrals of the form ∫-11 µ(t)φ(t)log(z-t)dt, with Jacobi weight µ and polynomial φ, and derives an estimate for the quadrature error that is asymptotic as n → ∞. The approach follows that previously described by Donaldson and Elliott. A numerical example illustrating the accuracy of the asymptotic estimate is presented. The extension of the theory to similar integrals defined on more general analytic arcs is outlined.