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In a previous paper by Lyness, an asymptotic expansion for the quadrature error functional for the «-dimensional simplex, valid when the integrand is an analytic function, was given. In this paper we develop the analogue of this result to cover the cases in which the integrand function has singularities of a specified nature at one or more vertices of the simplex.

Quadrature error functional expansions for the simplex when the integrand function has singularities at vertices