Quadrature formulas for integrals transforms generated by orthogonal polynomials

Details Quadrature formulas for integrals transforms generated by orthogonal polynomials Quadrature formulas for integrals transforms generated by orthogonal polynomials

2008-05-14

arxiv.org/abs/0805.2111v1

Mathematics

Numerical Analysis

3 figures, 11 pages

Scientific paper

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Transform in the case of the Hermite polynomials, a Bessel Transform in the case of the Laguerre polynomials and to an Appell Transform in the case of the Jacobi polynomials.

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