Gaussian quadrature theory

In Gaussian quadrature theory the NDF is called the weight function or measure. The weight function must be nonnegative and non-null in the integration interval and all its moments. 

The theory of Gaussian quadrature applies only to univariate distributions. However, in practical cases, the study of distributions with multiple internal coordinates is often necessary. In these cases the closure problem generally assumes the following form ... 

The interfacial width obtained from fitting the dPS-LDPE NR profiles is given in Table II. This measured interfacial width is described by a self-consistent mean-field theory, which is broadened by thermally excited capillary waves [2]. The measured interfacial width is given by Gaussian quadrature addition of the intrinsic (unbroadened by capillary waves) interfacial width, Ao, and the interfacial width associated with the capillary waves, Ac. This gives -... 

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