Quadrature formulas for Fourier-Chebyshev coefficients

Abstract

The aim of this work is to construct a new quadrature formula for Fourier-Chebyshev coefficients based on the divided differences of the integrand at points-1, 1 and the zeros of the nth Chebyshev polynomial of the second kind. The interesting thing is that this quadrature rule is closely related to the well-known Gauss-Turán quadrature formula and similar to a recent result of Micchelli and Sharma, extending a particular case due to Micchelli and Rivlin.