Fourier-Chebyshev Coefficients and Gauss-Turán Quadrature with Chebyshev Weight

Abstract

 The main purpose of this paper is to derive an explicit expression for Fourier-Chebyshev coefficient $A_{kn}(f)=\frac{\displaystyle 2}{\displaystyle\pi}\int_{-1}^1f(x)T_{kn}(x)\frac{\displaystyle dx}{\displaystyle \sqrt{1-x^2}},k,n\in N_0$, which is initiated by L. Gori and C. A. Micchelli.