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Mathematics of Computation

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Integral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions

Author: Sotirios E. Notaris
Journal: Math. Comp. 75 (2006), 1217-1231
MSC (2000): Primary 33C45, 65D32
Published electronically: May 1, 2006
MathSciNet review: 2219026
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Abstract: We evaluate explicitly the integrals $ \int_{-1}^{1}\pi_{n}(t)/(r\mp t)dt, \vert r\vert\neq 1$, with the $ \pi_{n}$ being any one of the four Chebyshev polynomials of degree $ n$. These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature formulae with Chebyshev abscissae, when the function to be integrated is analytic in a domain containing $ [-1,1]$ in its interior.

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Additional Information

Sotirios E. Notaris
Affiliation: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Zografou, Greece

Keywords: Integral formulas, Chebyshev polynomials, interpolatory quadrature formulae, error bounds
Received by editor(s): May 13, 2004
Received by editor(s) in revised form: October 3, 2004
Published electronically: May 1, 2006
Additional Notes: This work was supported in part by a grant from the Research Committee of the University of Athens, Greece, and in part by a “Pythagoras” O.P. Education grant to the University of Athens from the Ministry of National Education, Greece, and the European Union.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.