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Bounds for the Chebyshev functional and applications to the weighted integral formulae

The aim of this paper is to provide some error estimates for the general weighted n-point quadrature formulae by using some inequalities for the Chebyshev functional. The above results are applied to obtain some new bounds for the Gauss–Chebyshev formulae of the first and the second kind.

Chebyshev functional ; Grüss inequality ; Weighted quadrature formulae ; Gauss–Chebyshev formulae

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