Full Text:   <1067>

CLC number: O241.4

On-line Access: 

Received: 2001-07-03

Revision Accepted: 2001-10-26

Crosschecked: 0000-00-00

Cited: 0

Clicked: 2808

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

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

Share this article to: More

YANG Shi-jun. Quadrature formulas for Fourier-Chebyshev coefficients[J]. Journal of Zhejiang University Science A, 2002, 3(3): 327~331.

@article{title="Quadrature formulas for Fourier-Chebyshev coefficients",
author="YANG Shi-jun",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Quadrature formulas for Fourier-Chebyshev coefficients
%A YANG Shi-jun
%J Journal of Zhejiang University SCIENCE A
%V 3
%N 3
%P 327~331
%@ 1869-1951
%D 2002
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2002.0326

T1 - Quadrature formulas for Fourier-Chebyshev coefficients
A1 - YANG Shi-jun
J0 - Journal of Zhejiang University Science A
VL - 3
IS - 3
SP - 327
EP - 331
%@ 1869-1951
Y1 - 2002
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2002.0326

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Bojanov, B., 1996. On a quadrature formula of Micchelli and Rivlin. J. Comput. Appl. Math. 70:349-356.

[2] Gori, L., Miccheli, C.A., 1996. On weight functions which admit explicit Gauss-Turán quadrature formulas. Math. Computation, 65:1567-1581.

[3] Gradshteyn, I.S., Ryzhik, I.M., 1980. Table of Integrals, Series, and Products. New York Academic Press, New York.

[4] Hsu, L.C., Wang, X, 1983. Examples and methods in mathematical analysis. Higher Education Press, Beijing(in Chinese).

[5] Micchelli, C.A., Rivlin, T.J.,1972. Turán formulae and highest precision quadrature rules for Chebyshev coefficients, IBM J. Res. Develop.,16:372-379.

[6] Micchelli, C.A., Sharma, A., 1983. On a problem of Turán: multiple node Gaussian quadrature. Rendiconti di Mathematica Serie VII 3(3):529-552.

[7] Milovanovic, G.V.,1988. Construction of s-orthogonal polynomials and Turán quadrature formulae. In: Approx. Theory III, Nis. Ed. by G.V.Milonvic, Univ. Nis, p.311-328.

[8] Milovanovic, G.V.,2001. Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation. J. Comput. Appl. Math., 127:27-286.

[9] Shi, Y.G.,1995. A solution of problem 26 of P.Turán. Sci. China,38:1313-1319.

[10] Shi, Y.G.,1996. An analogue of problem 26 of P.Turán. Bull. Austral. Math. Soc.,53:1-12.

[11] Shi, Y.G.,1999. On some problems of P.Turán concerning Lm extremal polynomials and quadrature formulas. Journal of Approximation Theory, 100:203-220.

[12] Varma, A.K., Landau, E.,1995. New quadrature formulas based on the zeros of Jacobi polynomials. Computers Math. Applic. 30:213-220.

[13] Yang, S.J., Wang, X.H., 2002. Fourier-Chebyshev coefficients and Gauss-Turán quadrature with Chebyshev weight. Computers and mathematics with applications(accepted).

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE