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Journal of Zhejiang University SCIENCE A 2002 Vol.3 No.3 P.327-331


Quadrature formulas for Fourier-Chebyshev coefficients

Author(s):  YANG Shi-jun

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   yangshijun@mail.hz.zj.cn

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

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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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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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