Applied Scientific Research, Section B

, Volume 2, Issue 1, pp 33–45 | Cite as

On the method of saddle points

  • B. L. van der Waerden


If a complex integral is evaluated by the method of saddle points, a difficulty arises as soon as a pole lies near a saddle point. In this paper the saddle-point method will be developed in such a iorm that the part of the integral corresponding to the pole can be split off immediately. In addition to the usual terms an incomplete gamma Junction is found.


Saddle Point Branch Point Remainder Term Asymptotic Series Incomplete Gamma Function 
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).
    Sommerfeld, A., Ann. Physik28 (1909) 665;62 (1920) 95;84 (1926) 1135. See also his Partielle Differentialgleichungen der Physik (Vol.6 of Lectures on theoretical physics), chapter 6; Leipzig, 1948.CrossRefADSGoogle Scholar
  2. 2).
    Noether, F., Ausbreitung elektrischer Wellen über die Erde (Rothe-Ollendorff-Pohlhuasen, Funktionentheorie und ihre Anwendung in der Technik), part E, p. 154.Google Scholar
  3. 3).
    Weyl, H., Ann. Physik60 (1919) 481;62 (1920) 482.CrossRefADSGoogle Scholar
  4. 4).
    Ott, H., Ann. Physik43 (1943) 393.MATHCrossRefADSMathSciNetGoogle Scholar
  5. 5).
    Debye, P., Math. Ann.67 (1909) 535.MATHCrossRefMathSciNetGoogle Scholar
  6. 6).
    Rosen, J. Bark1ey, Theory and applications of\(\int {e - ^{x^2 } dx} \) Brooklyn, Mapleton House, 1948.Google Scholar

Copyright information

© Martinus Nijhoff 1952

Authors and Affiliations

  • B. L. van der Waerden
    • 1
  1. 1.Mathematisch CentrumAmsterdam

Personalised recommendations