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

Authors:	Sotirios E Notaris

Institution:	Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Zografou, Greece

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 . 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 in its interior.

Keywords:	Integral formulas Chebyshev polynomials interpolatory quadrature formulae error bounds

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