A Recursive algorithm by the moments method to evaluate a class of numerical integrals over an infinite interval

A special recursive algorithm is built by a three-term recursive formula with coefficients evaluated by the moments method. A new functional c(·) is studied over any function space that contains the polynomial space and it is shown that such a functional is positive definite, enabling us to use the advantages of such a property on the zeros of orthogonal polynomials for such a functional. A comparison is presented of the numerical advantages of such a method with respect to the Laguerre polynomials.