Weight functions for Chebyshev quadrature

Xu, Yuan

doi:10.1090/S0025-5718-1989-0970703-2

Weight functions for Chebyshev quadrature
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Math. Comp. 53 (1989), 297-302 Request permission

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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