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Quadratures and integral transforms arising from generating functions

Author

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  • Campos, Rafael G.
  • Marcellán, Francisco

Abstract

By using the explicit form of the eigenvectors of the finite Jacobi matrix associated to a family of orthogonal polynomials and some asymptotic expressions, we obtain quadrature formulas for the integral transforms arising from linear generating functions of the classical orthogonal polynomials. As a bypass product, we obtain simple and accurate Riemann–Steklov quadrature formulas and as an application of this quadrature formalism, we obtain the relationship between the fractional Fourier transform and the canonical coherent states.

Suggested Citation

  • Campos, Rafael G. & Marcellán, Francisco, 2017. "Quadratures and integral transforms arising from generating functions," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 8-18.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:8-18
    DOI: 10.1016/j.amc.2016.11.001
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    References listed on IDEAS

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    1. Rafael G. Campos & Rafael García Ruiz, 2013. "Fast Integration Of One-Dimensional Boundary Value Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(11), pages 1-10.
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    Cited by:

    1. Campos, Rafael G. & Huet, Adolfo, 2018. "Numerical inversion of the Laplace transform and its application to fractional diffusion," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 70-78.

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    1. Campos, Rafael G. & Huet, Adolfo, 2018. "Numerical inversion of the Laplace transform and its application to fractional diffusion," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 70-78.

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