GaussHermite interval quadrature rule ?
The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on R R is proved. Similar results have been recently obtained for the Jacobi weight on [?1,1] [ ? 1 , 1 ] and for the generalized Laguerre weight on [0,+?) [ 0 , + ? ) . Numerical construction of the GaussHermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few numerical examples are included.
hermite weight function weights interval gaussian quadrature rule nodes