Error of the Newton-Cotes and Gauss-Legendre Quadrature Formulas
نویسندگان
چکیده
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.
منابع مشابه
Error Estimates for Gauss Quadrature Formulas for Analytic Functions
1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...
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