Abstract: The aim of this work is to construct a new quadrature formula for Fourier-Chebyshev coef-ficients 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.

Key words: Divided differences, Quadrature, Chebyshev polynomials, Fourier-Chebyshev coefficient

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