On Gauss-Kronrod quadrature formulae of Chebyshev type. (English) Zbl 0768.41029
The author proves that there is no positive measure \(d\sigma\) on \((a,b)\) relativ to which the Gauss-Kronrod quadrature formula is also a Chebyshev quadrature formula. Also, he shows that there is no positive measure of the form \(d\sigma(t)=\omega(t)dt\), where \(\omega(t)\) is even, with symmetric support \((-a,a)\), for which the Gauss-Kronrod quadrature formula has equal weights for all \(n\) even. He also obtains that the Gauss-Kronrod quadrature rule is a special Chebyshev quadrature formula only if \(d\sigma(t)=(1-t^ 2)^{-1/2}dt\).
Reviewer: D.Acu (Sibiu)
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