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.
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Project supported by the Special Funds for Major State Basic Research(973) Programme of China (No. G19990328) and Zhejiang Provincial Natural Science Foundation, China (No. G100002)
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Yang, Sj. Quadrature formulas for Fourier-Chebyshev coefficients. J. Zheijang Univ.-Sci. A 3, 326–331 (2002). https://doi.org/10.1631/BF03396462
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DOI: https://doi.org/10.1631/BF03396462