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The remainder term for analytic functions of Gauss-Radau and Gauss- Lobatto quadrature rules with multiple end points. (English) Zbl 0724.41024
A study is undertaken of the kernels in the contour integral representation of the remainder terms for Gauss-Radau and Gauss-Lobatto quadrature rules over the interval [-1,1]. It is assumed that the respective end points in these rules have multiplicity two, and that integration is with respect to one of the four Chebyshev weight functions namely \((1-t^ 2)^{\pm}\), \((1-t)^{\pm}\), \((1+t)^{\mp}\). The points on the contour where the modulus of the kernel attains its maximum value are found for two of the weight functions. Numerical results are presented for the remaining weights. Only those elliptic contours which have foci at the points \(\pm 1\) are considered.

41A55 Approximate quadratures
Full Text: DOI
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