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numeric::gtdata

Weights and abscissae of Gauss-Tschebyscheff quadrature

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Syntax

numeric::gtdata(n)

Description

numeric::gtdata(n) returns the weights and the abscissae of the Gauss-Tschebyscheff quadrature rule with n nodes.

The Gauss-Tschebyscheff quadrature rule produces the exact integral for all integrands of the form with polynomials p(x) through degree 2 n - 1.

The exact weights b = [b1, …, bn] and abscissae c = [c1, …, cn] are given by

.

Environment Interactions

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

The function uses option remember.

Examples

Example 1

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

numeric::gtdata(2)

Parameters

n

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 exact weights and abscissae of the Gauss-Tschebyscheff quadrature rule, respectively.

Algorithms

The numerical integrator numeric::quadrature calls numeric::gtdata to provide the data for Gauss-Tschebyscheff quadrature.

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