Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T13:25:15.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear equations with elements (l/m)k(n/m) + δnm and infinitely many variables

Published online by Cambridge University Press:  24 October 2008

W. W. Wood
W. W. Wood
Affiliation:
Aeronautical Research Laboratories, Melbourne, Australia
Get access Rights & Permissions [Opens in a new window]

Extract

Introduction. Infinite systems

are discussed in which k(θ) and b(n) are differentiable. The aim is to determine the behaviour of a(n) for large n and to reduce (1) to a finite system. This involves solving

for the high order a(n), n ≥ N, in terms of the preceding a(n), with a large enough N to facilitate the iteration procedure employed. The desired N − 1, N − 1 system follows on substitution for the high order a(n) in the first N − 1 equations (1).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 3 , July 1965 , pp. 781 - 794
Copyright
Copyright © Cambridge Philosophical Society 1965

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)Cherry, T. M. (TO appear.)Google Scholar
(2)Krein, M. G.Integral equations on a half line, with kernel depending on the difference of the arguments. Amer. Math. Soc. Transl. 22 (1962), 163–288.Google Scholar
(3)Titchmarsh, E. C.Introduction to the theory of Fourier integrals (Oxford, 1937).Google Scholar
(4)Wood, W. W.Properties of inviscid, recirculating flows. J. Fluid Mech. (to appear).Google Scholar