Abstract
By applying the theory of completely symmetric functions we derive a Gaussian quadrature rule which generalizes that due to McNamee. A feature of this generalization is the inclusion of an explicit correction term taking account of the presence of poles (of any order) of the integrand close to the integration-interval. A numerical example is provided to illustrate the formulae.
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Hunter, D.B., Okecha, G.E. A modified Gaussian quadrature rule for integrals involving poles of any order. BIT 26, 233–240 (1986). https://doi.org/10.1007/BF01933749
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DOI: https://doi.org/10.1007/BF01933749