Gauss–Hermite interval quadrature rule

The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on RR 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 Gauss–Hermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few numerical examples are included.