On stratified extensions of Gauss–Laguerre and Gauss–Hermite quadrature formulas

For the practical estimation of the error of Gauss–Laguerre and Gauss–Hermite quadrature formulas, it is well known that real positive Kronrod formulas do not exist. Among the alternatives which are available in the literature, the stratified rules introduced by Laurie are of particular interest. In this note, we determine the degree optimal stratified extensions for the Gauss–Laguerre and Gauss–Hermite formulas, and we investigate their properties.