Abstract
The error in the classical interpolatory (including Gaussian) numerical integration rules for analytic functions can be considered to be due to a ‘pole’ at infinity. The residue of this ‘pole’ is approximately taken into account by using Taylor-Maclaurin series expansions at the origin- and asymptotic expansions at infinity. The computer algebra system Maple V was found appropriate and used in this task. The cases of the Gauss-Chebyshev and the Gauss-Legendre quadrature rules were considered in some detail. Finally, numerical results in applications both for regular and for Cauchy-type principal value integrals are also presented and the strong improvement in the numerical results by the present approach is illustrated.
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