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Approximate integration of rapidly oscillating functions and of periodic functions

Published online by Cambridge University Press:  24 October 2008

L. C. Hsu
L. C. Hsu
Affiliation:
Mathematics Department, Jilin University (North-East People's University), Changchun, China
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Extract

The purpose of this paper is to establish a few approximation formulae with error estimates for the integration of rapidly oscillating functions, and to present an expression for the remainder term of an expansion formula obtained previously (see (3)). Moreover, we shall give a certain sharpest possible estimation for the error term involved in the numerical integration of periodic functions. Some results contained in earlier papers ((2), (4), (5)) will be employed and sharpened.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 81 - 88
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Hammer, P. C. and Wymore, A. W.Math. Tables Aids Comput. 11 (1957), 59.Google Scholar
(2)Hsu, L. C.Tohoku Math. J. 9 (1957), 45.Google Scholar
(3)Hsu, L. C.Sci. Record (N.S., Academia Sinica), 2 (1958), 193.Google Scholar
(4)Hsu, L. C.Sci. Record (N.S., Academia Sinica), 3 (1959), 544.Google Scholar
(5)Hsu, L. C.Numer. Math. 3 (1961), 169.CrossRefGoogle Scholar
(6)Milne-Thomson, L. M.Calculus of finite differences (Macmillan: London, 1933).Google Scholar