MKl wrote:
I'm using the routine gqgenerategaussjacobi to generate points and weights for Gauss-Jacobi integration. When debugging my code I observed that the weights of the generated rules don't add up to 1, but rather to 1.0666...
It's alright. Sum of weights is equal to integral(a,b,1*W(x)dx) (try to calculate this integral using Gauss-Jacobi formula and you will see why).
This integral is equal to 2.0 only in the Gauss-Legendre case (alpha=beta=0.0).
Note - to 2.0, not to 1.0. In the general case it may have arbitrary value.