Weights and abscissae of Newton-Cotes quadrature

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numeric::ncdata(n) returns the weights and the abscissae of the Newton-Cotes quadrature rule with n equidistant nodes.

The Newton-Cotes quadrature rule produces the exact integral for all polynomials f through degree n - 1. If n is odd, then the quadrature rule is exact through degree n.

The equidistant abscissae c = [c1, …, cn] are given by .

Environment Interactions

numeric::ncdata is not sensitive to the environment variable DIGITS.

The function uses option remember.


Example 1

The following call produces exact data for the quadrature rule with four nodes:




The number of nodes: a positive integer

Return Values

List [b,c] is returned. The lists b = [b1, …, bn] and c = [c1, …, cn] are the rational weights and abscissae of the Newton-Cotes quadrature rule, respectively.


The numerical integrator numeric::quadrature calls numeric::ncdata to provide the data for Newton-Cotes quadrature.