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Asymptotic Expansions of the Modified Bessel Function of the Third Kind of Imaginary Order

1967; Society for Industrial and Applied Mathematics; Volume: 15; Issue: 5 Linguagem: Inglês

10.1137/0115114

1095-712X

Charles B. Balogh,

Electrical and Electromagnetic Research

Previous article Next article Asymptotic Expansions of the Modified Bessel Function of the Third Kind of Imaginary OrderCharles B. BaloghCharles B. Baloghhttps://doi.org/10.1137/0115114PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Charles B. Balogh, Uniform asymptotic expansions of the modified Bessel function of the third kind of large imaginary order, Bull. Amer. Math. Soc., 72 (1966), 40–43 MR0188504 0134.28904 CrossrefISIGoogle Scholar[2] F. G. Friedlander, Diffraction of pulses by a circular cylinder, Comm. Pure Appl. Math., 7 (1954), 705–732 MR0066182 0057.18701 CrossrefISIGoogle Scholar[3] N. N. Lebedev, Sur un formule d'inversion, C. R. (Doklady) Acad. Sci. URSS (N.S.), 52 (1946), 655–658 MR0021144 0063.03462 Google Scholar[4] Wilhelm Magnus, , Fritz Oberhettinger and , Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition. Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966viii+508 MR0232968 0143.08502 CrossrefGoogle Scholar[5] F. W. J. Olver, The asymptotic solution of linear differential equations of the second order for large values of a parameter, Philos. Trans. Roy. Soc. London. Ser. A., 247 (1954), 307–327 MR0067249 0070.30801 CrossrefGoogle Scholar[6] F. W. J. Olver, The asymptotic expansion of Bessel functions of large order, Philos. Trans. Roy. Soc. London. Ser. A., 247 (1954), 328–368 MR0067250 0070.30801 CrossrefGoogle Scholar[7] F. W. J. Olver, Error bounds for first approximations in turning-point problems, J. Soc. Indust. Appl. Math., 11 (1963), 748–772 10.1137/0111057 MR0160981 0118.32902 LinkISIGoogle Scholar[8] F. W. J. Olver, Error bounds for asymptotic expansions in turning-point problems, J. Soc. Indust. Appl. Math., 12 (1964), 200–214 10.1137/0112019 MR0163003 0123.04803 LinkISIGoogle Scholar[9] Enok Palm, On the zeros of Bessel functions of pure imaginary order, Quart. J. Mech. Appl. Math., 10 (1957), 500–503 MR0092872 0081.29304 CrossrefGoogle Scholar[10] G. Pólya, On the zeros of certain trigonometric integrals, J. London Math. Soc., 1 (1926), 98–99 CrossrefGoogle Scholar[11] Waldemar Schöbe, Eine an die Nicholsonformel anschliessende asymptotische Entwicklung für Zylinderfunktionen, Acta Math., 92 (1954), 265–307 MR0067251 0057.05501 CrossrefISIGoogle Scholar[12] British Association for the Advancement of Science, Bessel functions. Part II. Functions of positive integer order, British Association for the Advancement of Science, Mathematical Tables, vol. X, University Press, Cambridge, 1952xl+255 MR0050973 0049.09409 Google Scholar[13] Milton Abramowitz and , Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, Vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964xiv+1046 MR0167642 0171.38503 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Eisenstein series and an asymptotic for the K-Bessel function8 April 2021 | The Ramanujan Journal, Vol. 56, No. 1 Cross Ref On quantum corrections to geodesics in de-Sitter spacetime25 February 2021 | The European Physical Journal C, Vol. 81, No. 2 Cross Ref Large values of cusp forms on $$\mathrm {GL}_n$$9 September 2020 | Selecta Mathematica, Vol. 26, No. 4 Cross Ref LOW‐LYING ZEROS OF L ‐FUNCTIONS FOR MAASS FORMS OVER IMAGINARY QUADRATIC FIELDS13 May 2020 | Mathematika, Vol. 66, No. 3 Cross Ref On the global sup-norm of GL(3) cusp forms2 February 2019 | Israel Journal of Mathematics, Vol. 229, No. 1 Cross Ref A note on the sup norm of Eisenstein series11 April 2018 | The Quarterly Journal of Mathematics, Vol. 15 Cross Ref Sup-norm bounds for Eisenstein seriesForum Mathematicum, Vol. 29, No. 6 Cross Ref The horocycle flow at prime timesJournal de Mathématiques Pures et Appliquées, Vol. 103, No. 2 Cross Ref Nodal Domains of Maass Forms I9 July 2013 | Geometric and Functional Analysis, Vol. 23, No. 5 Cross Ref Bounds and algorithms for the -Bessel function of imaginary order10 April 2013 | LMS Journal of Computation and Mathematics, Vol. 16 Cross Ref Semiclassical Low Energy Scattering for One-Dimensional Schrödinger Operators with Exponentially Decaying Potentials29 December 2011 | Annales Henri Poincaré, Vol. 13, No. 6 Cross Ref Spontaneous Excitation of an Accelerated Detector Interacting with a Massive Scalar Field and Unruh Effect14 March 2012 | Communications in Theoretical Physics, Vol. 57, No. 3 Cross Ref On Pointwise Decay of Linear Waves on a Schwarzschild Black Hole Background26 November 2011 | Communications in Mathematical Physics, Vol. 309, No. 1 Cross Ref Relativistic accelerating electromagnetic waves29 September 2011 | Journal of Optics, Vol. 13, No. 10 Cross Ref Error bounds for uniform asymptotic expansions—modified bessel function of purely imaginary order25 August 2010 | Chinese Annals of Mathematics, Series B, Vol. 31, No. 5 Cross Ref Bounding sup-norms of cusp forms of large level11 December 2009 | Inventiones mathematicae, Vol. 179, No. 3 Cross Ref Light scattering characteristics and the factor of radiation pressure efficiency for a spherical microcenter of optical breakdown laser plasma20 March 2009 | Atmospheric and Oceanic Optics, Vol. 22, No. 1 Cross Ref CLASSICAL AND QUANTUM FEATURES OF THE MIXMASTER SINGULARITY26 April 2012 | International Journal of Modern Physics A, Vol. 23, No. 16n17 Cross Ref Defects in nematic membranes can buckle into pseudospheres15 April 2008 | Physical Review E, Vol. 77, No. 4 Cross Ref Dynamo Effect in the Kraichnan Magnetohydrodynamic Turbulence28 September 2007 | Journal of Statistical Physics, Vol. 129, No. 2 Cross Ref Inhomogeneous quantum Mixmaster: from classical towards quantum mechanics8 December 2006 | Classical and Quantum Gravity, Vol. 24, No. 2 Cross Ref Effective computation of Maass cusp forms1 January 2006 | International Mathematics Research Notices, Vol. 15 Cross Ref On the uniform equidistribution of long closed horocyclesDuke Mathematical Journal, Vol. 123, No. 3 Cross Ref Computing solutions of the modified Bessel differential equation for imaginary orders and positive argumentsACM Transactions on Mathematical Software, Vol. 30, No. 2 Cross Ref Asymptotic relations among Fourier coefficients of automorphic eigenfunctions22 September 2003 | Transactions of the American Mathematical Society, Vol. 356, No. 2 Cross Ref Algorithms and codes for the Macdonald function: recent progress and comparisonsJournal of Computational and Applied Mathematics, Vol. 161, No. 1 Cross Ref Laplace's method on a computer algebra system with an application to the real valued modified Bessel functionsJournal of Computational and Applied Mathematics, Vol. 146, No. 2 Cross Ref On Eigenfunctions of the Laplacian for Hecke Triangle Groups Cross Ref On the Topography of Maass Waveforms for PSL(2, Z)Experimental Mathematics, Vol. 1, No. 4 Cross Ref On acoustic transmission in ocean-surface waveguides1 January 1997 | Philosophical Transactions of the Royal Society of London. 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