Quadrature formulas for integrals transforms generated by orthogonal polynomials

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Authors
Campos, Rafael G.
Mota, Francisco Dominguez
Coronado, E.
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Abstract
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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.
Comment: 3 figures, 11 pages
Keywords
Mathematics - Numerical Analysis, 33C45, 33C47, 44A20, 65D32
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