Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase
A. Erdélyi · Journal of the Society for Industrial and Applied Mathematics · 1955
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 SectionsAbout[1] E. T. Copson, The asymptotic expansion of a function defined by a definite integral or contour integral, Admiralty Computing Service, London, 1946 Google Scholar[2] J. G. Van Der Corput, Zur Methode der stationären Phase. I, Compositio Math., 1 (1934), 15–38 Google Scholar[3] J. G. van der Corput, Zur Methode der stationären Phase. II, Compositio Math., 3 (1936), 328–372 0015.01103 Google Scholar[4] 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 Scholar[5] Gustav Doetsch, Handbuch der Laplace-Transformation. Band I. Theorie der Laplace-Transformation, Verlag Birkhäuser, Basel, 1950, 581– MR0043253 0040.05901 CrossrefGoogle Scholar[6] 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 Scholar[7] H. Poincaré, Sur la diffraction des ondes électriques, Proc. Roy. Soc., 72 (1904), 42–52 CrossrefGoogle Scholar[8] 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 Scholar[9] 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