Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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 $ x$, are obtained for the representative Fourier integral $ \int_0^\infty {A\left( k \right) \exp \left( {ikx} \right) dk}$ for a variety of asymptotic forms of behaviour of the function $ A\left( k \right)$, 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.


References [Enhancements On Off] (What's this?)

  • [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] Eugene Jahnke and Fritz Emde, Tables of Functions with Formulae and Curves, Dover Publications, New York, 1943. MR 0008332
  • [4] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469

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DOI: https://doi.org/10.1090/qam/233132
Article copyright: © Copyright 1968 American Mathematical Society


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