11.1 One-Dimensional Gauss–Hermite Quadrature

The objective now is to expand imgimg in terms of orthogonal polynomials in some way. First, consider the one-dimensional case integral of the form

(11.6) equation

Expanding img in a general set of orthogonal polynomials, img can be approximated by

(11.7) equation

where {img represent a set of orthogonal polynomials, with the polynomials img and img orthogonal with respect to a weight (or kernel) function img over the interval such that

(11.8)

Here, cl is a normalization constant and

(11.9) ...

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