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Quadrature formulas for Fourier-Chebyshev coefficients
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YANG Shi-jun. Quadrature formulas for Fourier-Chebyshev coefficients[J]. Journal of Zhejiang University Science A, 2002, 3(3): 327-331.
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author="YANG Shi-jun",
journal="Journal of Zhejiang University Science A",
volume="3",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0326"
}
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J0 - Journal of Zhejiang University Science A
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DOI - 10.1631/jzus.2002.0326
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.
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