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Error of the Newton-Cotes and Gauss-Legendre quadrature formulas


Author: N. S. Kambo
Journal: Math. Comp. 24 (1970), 261-269
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1970-0275671-2
MathSciNet review: 0275671
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Abstract: It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polynomial and the Legendre function of the second kind are obtained. These bounds are employed to derive a bound on the error of the Gauss-Legendre quadrature formula for analytic functions.


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DOI: https://doi.org/10.1090/S0025-5718-1970-0275671-2
Keywords: Newton-Cotes quadrature formula, Cotes numbers, Legendre polynomial, Legendre function of the second kind, Gauss-Legendre quadrature formula, error bound, asymptotic bound, Davis' method
Article copyright: © Copyright 1970 American Mathematical Society