# Newton-Cotes formulas

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## Newton-Cotes formulas

[′nüt·ən ′kōts ‚fȯr·myə·ləz]
(mathematics)
Approximation formulas for the integral of a function along a small interval in terms of the values of the function and its derivatives.
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If a quadrature formula is used, Equation (26) becomes
Namely, the domain was divided into sufficiently small intervals where the 64-point Gauss-Legendre quadrature formula is appropriate for the purpose.
By using the q-binomial theorem, we have recently obtained explicit expressions of the coefficients [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the quadrature formula 
m] admits an n-point (ordinary) Gaussian quadrature formula
An RMS rule is a symmetric interpolatory quadrature formula on [-1,1], hereafter denoted by the set of its nonnegative nodes.
Turin  proposed an interpolatory quadrature formula of the type
Moreover, it was proved that the Lebesgue constant of such angles is O (log n) and that the associated interpolatory trigonometric quadrature formula has positive weights.
m], it is an easy matter to derive a quadrature formula based on interpolation to value and slope at [x.
Let n,p, s [member of] N such that s < p + 1, and consider the spherical quadrature formula (2.
k=1] be the nodes and the weights of an m-point Gaussian quadrature formula on [0,1].

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