Integral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions
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- by Sotirios E. Notaris PDF
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Abstract:
We evaluate explicitly the integrals $\int _{-1}^{1}\pi _{n}(t)/(r\mp t)dt,\ |r|\neq 1$, 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.References
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Additional Information
- Sotirios E. Notaris
- Affiliation: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Zografou, Greece
- Email: notaris@math.uoa.gr
- 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.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 75 (2006), 1217-1231
- MSC (2000): Primary 33C45, 65D32
- DOI: https://doi.org/10.1090/S0025-5718-06-01859-X
- MathSciNet review: 2219026