Relationship to orthogonal polynomials

A convenient choice for univariate EQMOM is to define 6a (x, y) in terms of the weight function w(t) for a known family of orthogonal polynomials (Gautschi, 2004). For example, on the interval [0, oo) the associated Laguerre polynomials have the weight function 

The fact that the Jacobi matrix is known can be used to evaluate very accurately integrals involving 6a (x,y) by applying Gaussian quadrature. For example, Eq. (3.84) leads to 

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