#include <deal.II/base/quadrature_lib.h>

Inheritance diagram for QGaussChebyshev< dim >:

Public Member Functions
	QGaussChebyshev (const unsigned int n)
	Generate a formula with `n` quadrature points.

	QGaussChebyshev (const unsigned int n)

Detailed Description

template<int dim>
class QGaussChebyshev< dim >

Gauss-Chebyshev quadrature rules integrate the weighted product $\int_{-1}^1 f(x) w(x) dx$ with weight given by: $w(x) = 1/\sqrt{1-x^2}$ . The nodes and weights are known analytically, and are exact for monomials up to the order $2n-1$ , where $n$ is the number of quadrature points. Here we rescale the quadrature formula so that it is defined on the interval $[0,1]$ instead of $[-1,1]$ . So the quadrature formulas integrate exactly the integral $\int_0^1 f(x) w(x) dx$ with the weight: $w(x) = 1/\sqrt{x(1-x)}$ . For details see: M. Abramowitz & I.A. Stegun: Handbook of Mathematical Functions, par. 25.4.38