ChebyshevGauss quadrature, also called Chebyshev quadrature, is a Gaussian quadrature over the interval with weighting function (Abramowitz and Stegun 1972, p. 889). The abscissas for quadrature order are given by the roots of the Chebyshev polynomial of the first kind , which occur symmetrically about 0. The weights are
(1)
 
(2)

where is the coefficient of in ,
(3)

and the order Lagrange interpolating polynomial for .
For Chebyshev polynomials of the first kind,
(4)

so
(5)

Additionally,
(6)

so
(7)

Since
(8)

the abscissas are given explicitly by
(9)

Since
(10)
 
(11)

where
(12)

all the weights are
(13)

The explicit formula is then
(14)

The following two tables give the numerical and analytic values for the first few points and weights.
2  1.5708  
3  0  1.0472 
1.0472  
4  0.785398  
0.785398  
5  0  0.628319 
0.628319  
0.628319 
2  
3  0  
3  
4  
4  
5  0  
5  
5 