Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase

Previous article Next article Asymptotic Representations of Fourier Integrals and the Method of Stationary PhaseA. ErdelyiA. Erdelyihttps://doi.org/10.1137/0103002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 E. T. Copson, The asymptotic expansion of a function defined by a definite integral or contour integral, Admiralty Computing Service, London, 1946 Google Scholar2 J. G. Van Der Corput, Zur Methode der stationären Phase. I, Compositio Math., 1 (1934), 15–38 Google Scholar3 J. G. van der Corput, Zur Methode der stationären Phase. II, Compositio Math., 3 (1936), 328–372 0015.01103 Google Scholar4 J. G. van der Corput, On the method of critical points. I, Nederl. Akad. Wetensch., Proc., 51 (1948), 650–658 = Indagationes Math. 10, 201–209 (1948) MR0026141 0030.24601 Google Scholar5 Gustav Doetsch, Handbuch der Laplace-Transformation. Band I. Theorie der Laplace-Transformation, Verlag Birkhäuser, Basel, 1950, 581– MR0043253 0040.05901 CrossrefGoogle Scholar6 Lord Kelvin, On the waves produced by a single impulse in water of any depth, or in a dispersive medium, Philos. Mag., 23 (1887), 252–255, Math. and Phys. Papers, vol. 4 (1910), 303–306 CrossrefGoogle Scholar7 H. Poincaré, Sur la diffraction des ondes électriques, Proc. Roy. Soc., 72 (1904), 42–52 CrossrefGoogle Scholar8 G. G. Stokes, On the numerical calculation of a class of definite integrals and infinite series, Cambridge Philos. Trans., 9 (1856), 166–187, Math. and Phys. Papers, vol. 2 (1883), 329–357. Google Scholar9 G. N. Watson, The limits of applicability of the principle of stationary phase, Proc. Cambridge Philos. Soc., 19 (1918), 49–55 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Fourier-Cosine Method for Finite-Time Gerber--Shiu FunctionsXiaolong Li, Yifan Shi, Sheung Chi Phillip Yam, and Hailiang Yang27 May 2021 | SIAM Journal on Scientific Computing, Vol. 43, No. 3AbstractPDF (1078 KB)Diffraction of Waves on Square Lattice by Semi-Infinite CrackBasant Lal Sharma11 June 2015 | SIAM Journal on Applied Mathematics, Vol. 75, No. 3AbstractPDF (1994 KB)Error Bounds for Stationary Phase ApproximationsF. W. J. Olver1 August 2006 | SIAM Journal on Mathematical Analysis, Vol. 5, No. 1AbstractPDF (800 KB)Asymptotic Behavior of IntegralsD. S. Jones18 July 2006 | SIAM Review, Vol. 14, No. 2AbstractPDF (2577 KB)On the Method of Stationary Phase for Multiple IntegralsF. de Kok17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 2, No. 1AbstractPDF (1518 KB)Note on Asymptotic Expansions of Fourier Integrals Involving Logarithmic SingularitiesJames McKenna13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 15, No. 4AbstractPDF (167 KB)Asymptotic Expansions of Fourier Integrals Involving Logarithmic SingularitiesA. Erdélyi10 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 4, No. 1AbstractPDF (637 KB) Volume 3, Issue 1| 1955Journal of the Society for Industrial and Applied Mathematics History Submitted:11 January 1955Published online:10 July 2006 InformationCopyright © 1955 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0103002Article page range:pp. 17-27ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics