Series representations of Fourier integrals
Authors:
H. C. Levey and J. J. Mahony
Journal:
Quart. Appl. Math. 26 (1968), 101-109
MSC:
Primary 41.50
DOI:
https://doi.org/10.1090/qam/233132
MathSciNet review:
233132
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Abstract: General series representations, valid at least for small values of , are obtained for the representative Fourier integral
for a variety of asymptotic forms of behaviour of the function
, assumed bounded and integrable in any finite range. The results obtained should be of value in the numerical evaluation of such integrals as well as in the determination of their analytic properties.
- [1] H. C. Levey, The generation and propagation of an undular jump, Proceedings of Second Australasian Conference on Hydraulics and Fluid Mechanics, Auckland, 1965
- [2] M. J. Lighthill, Fourier integrals and generalized functions, Cambridge Univ. Press, New York, 1959
- [3] E. Jahnke and F. Emde, Tables of functions, Dover, New York, 1943 MR 0008332
- [4] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Univ. Press, New York, 1946 MR 1424469
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Additional Information
DOI:
https://doi.org/10.1090/qam/233132
Article copyright:
© Copyright 1968
American Mathematical Society