Archive for Rational Mechanics and Analysis

, Volume 14, Issue 1, pp 217–260 | Cite as

The asymptotic evaluation of certain integrals

  • A. Erdélyi
  • M. Wyman


Asymptotic Behavior Asymptotic Expansion Critical Region Airy Function Asymptotic Equality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Erdélyi, A.: General Asymptotic Expansions of Laplace Integrals. Arch. Rational Mech. Anal. 7, 1–20 (1961).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Erdélyi, A.: Asymptotic Solutions of Differential Equations with Transition Points or Singularities. J. of Math. Phys. 1, 16–26 (1960).ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Schmidt, H.: Beiträge zu einer Theorie der allgemeinen asymptotischen Darstellungen. Math. Ann. 113, 629–656 (1936).CrossRefzbMATHGoogle Scholar
  4. [4]
    Perron, O.: Über die näherungsweise Berechnung von Funktionen großer Zahlen. Sitzungsber. d. Bayr. Akad. d. Wissensch. (Munch. Ber.) 1917, S. 191–219.Google Scholar
  5. [5]
    Wyman, M.: The Asymptotic Behavior of the Hermite Polynomials. Can. J. of Math. 15, 332–349 (1963).CrossRefzbMATHGoogle Scholar
  6. [6]
    Darboux, G.: Mémoire sur l'approximation des fonctions de très-grands nombres, et sur une classe étendue de développements en série. J. de Mathématiques pures et appliquées, Series 3, 4, 5–56, 377–416 (1878).Google Scholar
  7. [7]
    Miller, J. C. P.: The Airy Integral, B. A. S. A. Math. Tables, vol. B. New York: Cambridge University Press 1946.Google Scholar
  8. [8]
    Olver, F. W. J.: The asymptotic solution of linear differential equations of the second order for large values of a parameter and the asymptotic expansion of Bessel Functions of large order. Phil. Trans. Roy. Soc. (London), A 247, 307–368 (1954).ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    Corput, J. G. Van Der: On the method of critical points. I. Proc. Nederl. Akad. Wetensch. 51, 650–658 (1948).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1963

Authors and Affiliations

  • A. Erdélyi
    • 1
    • 2
  • M. Wyman
    • 1
  1. 1.California Institute of TechnologyPasadena
  2. 2.University of AlbertaEdmonton

Personalised recommendations