Quadratures and integral transforms arising from generating functions

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.