A quadrature formula of Clenshaw–Curtis type for the Gegenbauer weight-function

We investigate a method for the numerical evaluation of integrals over [ - 1 , 1 ] of functions of the form ( 1 - x 2 ) λ - 1 / 2 f ( x ) , based on approximating f ( x ) by a finite Chebyshev expansion. Error bounds are obtained, and the method is illustrated by an example.