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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
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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

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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