Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-20T04:22:53.580Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical evaluation of the integral

Published online by Cambridge University Press:  24 October 2008

Diana Catton  and
B. G. Millis
Diana Catton
Affiliation:
University Mathematical LaboratoryCambridge
B. G. Millis
Affiliation:
University Mathematical LaboratoryCambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical values of the above integral are given for 3/2λ√3 = 0(0·1)1, to six decimals for |ω| = 0(0·l)2·0(0·2)4·8 and to seven decimals for |ω| = 5(0·5)10(1)15.

The integral satisfies a third-order differential equation; this equation is integrated numerically for ω ≥ 0 and ω ≤ 0, and in each case the method of isolating the solution which satisfies f(ω) → 0 as ω → ∞ is described.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 4 , October 1958 , pp. 454 - 462
Copyright
Copyright © Cambridge Philosophical Society 1958

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Longuet-Higgins, M. S.The statistical distribution of the curvature of a random Gaussian surface. Proc. Camb. Phil. Soc. 54 (1958), 439–53.Google Scholar
(2)Hayashi, K.Tafeln der Besselschen, Theta, Kugel und anderer Funktionen (Berlin, 1930).Google Scholar
(3)Hayashi, K.Tafeln fur die Differenzenrechnung (Berlin, 1933).Google Scholar
(4)Gray, A., Mathews, G. B. and MacRobert, T. M.Bessel functions (London, 1922), pp. 313–315.Google Scholar
(5)British Association Mathematical Tables. Vol. vi. Bessel functions. Part I. Functions of order zero and unity (Cambridge, 1937).Google Scholar
(6)Gill, S.A process for the step-by-step integration of differential equations in an automatic digital computing machine. Proc. Camb. Phil. Soc. 47 (1951), 96–108.Google Scholar