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- W2019925222 abstract "The note A constant in the theory of trigonometric series in the October 1964 issue of Mathematics of Computation provided us with a test for our recently constructed algorithms for the computation of roots of functions, and for numerical quadrature in the presence of singularities. The latter algorithm, utilizing the Gaussian 8-point quadrature formula applied to sub-intervals of variable length, involves a sufficiently small number of ordinates that computational labor and round-off error do not become problems. Use of these algorithms indicated the value ao = .3084438, for the root of the equation fJot2 u cos u du = 0, differing from the reported value, .30483, in the third place. To check this result, we made the transformation u = X4 to weaken the character of the singularity at the origin, and obtained the following table by conventional numerical quadrature, confirming our result:" @default.
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- W2019925222 date "1965-09-01" @default.
- W2019925222 modified "2023-10-17" @default.
- W2019925222 title "On a constant in the theory of trigonometric series" @default.
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- W2019925222 doi "https://doi.org/10.1090/s0025-5718-65-99245-8" @default.
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