The Convergence Rate on a Quadrature of a Fourier Integral with Symmetrical Jacobi Weight for an Analytical Function

Abstract

In this paper, through complex analysis, the convergence rate is given on a quadrature of a Fourier integral with symmetrical Jacobi weight. The interpolation nodes of this quadrature formula are expressed by the frequency, and the coefficients can be expressed by the Bessel function. When the frequency is close to 0, the nodes are close to those in the Gauss quadrature. When the frequency tends to infinity, the nodes tend symmetrically to the two ends of the integrand. The higher the frequency is, the higher the accuracy of this quadrature will be. Numerical examples are provided to illustrate the theoretical results.