On the Gaussian integration of Chebyshev polynomials

Curtis, A. R.; Rabinowitz, P.

doi:10.1090/S0025-5718-1972-0298934-5

On the Gaussian integration of Chebyshev polynomials
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by A. R. Curtis and P. Rabinowitz PDF

Math. Comp. 26 (1972), 207-211 Request permission

Abstract:

It is shown that as $m$ tends to infinity, the error in the integration of the Chebyshev polynomial of the first kind, ${T_{(4m + 2)j \pm 2l}}(x)$, by an $m$-point Gauss integration rule approaches ${( - 1)^j} \cdot 2/(4{l^2} - 1),l = 0,1, \cdots ,m - 1$, and ${( - 1)^j} \cdot \pi /2,l = m$, for all $j$.

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