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III.—On a Quadrature Formula for Trigonometric Integrals

Published online by Cambridge University Press:  15 September 2014

L. N. G. Filon
L. N. G. Filon
Affiliation:
University College, London
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Extract

1. Integrals of the form where ψ(x) is a function with a limited number of turning-points in the range of integration and k is a constant which may take up large values, frequently occur in investigations in mathematical physics, and their computation by quadratures is often desirable.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 49 , 1930 , pp. 38 - 47
Copyright
Copyright © Royal Society of Edinburgh 1930

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References

page 44 note * Tables of sin xdx/x have been calculated by Glaisher, J. W. L., in Phil. Trans., 1870, p. 367Google Scholar, up to x = 15. Tables have also been constructed for various greater values of x. See B.A. Report (1927), pp. 245–251, and B.A. Report (1928).