Quadratures and integral transforms arising from generating functions Articles uri icon

publication date

  • March 2017

start page

  • 8

end page

  • 18

volume

  • 297

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

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. (C) 2016 Elsevier Inc. All rights reserved.

keywords

  • integral transforms; quadratures; orthogonal polynomials; generating functions; fourier-transform; expansions; states