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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Weight functions for Chebyshev quadrature

Author: Yuan Xu
Journal: Math. Comp. 53 (1989), 297-302
MSC: Primary 65D32
MathSciNet review: 970703
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Abstract: In this paper, we investigate if the weight function ${(1 - {x^2})^{ - 1/2}}R(x)$, where $R(x)$ is a rational function of order (1,1), admits Chebyshev quadratures. Many positive examples are provided. In particular, we have proved that the answer is affirmative if $R(x) = 1 + bx$, $|b| < 0.27846 \ldots$.

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Keywords: Chebyshev quadrature, weight function with property <I>T</I>
Article copyright: © Copyright 1989 American Mathematical Society