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Some error expansions for certain Gaussian quadrature rules. (English) Zbl 1025.41018
The author obtains the coefficients of the error term for the Gaussian quadrature rule which is derived by R. Kumar [J. Inst. Math. Appl. 14, 175-182 (1974; Zbl 0287.65015)]. In addition, he gives a numerical example and compares the results.

MSC:
41A55 Approximate quadratures
41A80 Remainders in approximation formulas
41A50 Best approximation, Chebyshev systems
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References:
[1] M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions, Dover, New York, 1966.
[2] Clenshaw, C.W.; Curtis, A.R., A method for the numerical integration on an automatic computer, Numer. math., 2, 197-205, (1960) · Zbl 0093.14006
[3] Hunter, D.B., Some error expansions for Gaussian quadrature, Bit, 35, 64-82, (1995) · Zbl 0824.41032
[4] Kumar, R., Certain Gaussian quadratures, Jour. I.M.A., 14, 175-182, (1974) · Zbl 0287.65015
[5] H.V. Smith, Numerical Methods of Integration, Chartwell-Bratt, Bromley, 1993. · Zbl 0828.65014
[6] Smith, H.V., A correction term for gauss – legendre quadrature, Internat. J. math. ed. sci. tech., 34, 53-56, (2003)
[7] Stenger, F., Bounds on the error of Gauss-type quadratures, Numer. math., 8, 150-160, (1966) · Zbl 0149.12002
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