, Volume 21, Issue 1, pp 105-109

Some positive cotes numbers for the chebyshev weight function

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Abstract

We show that, for the Chebyshev weight function (1−x 2)−1/2, the Cotes numbers for the quadrature rule with nodes at the zeros of the ultraspherical polynomialP n /(λ) are nonnegative if and only if −1/2<λ≤1.