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A Matrix Representation of Ascending and Descending Continued Fractions1

Published online by Cambridge University Press:  20 January 2009

L. M. Milne-Thomson
L. M. Milne-Thomson
Affiliation:
(Greenwich)
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The present paper describes briefly a notation for representing continued fractions in many dimensions, which has the advantage providing a direct method of attack and of rendering intuitive, results which are usually proved by induction. The notation is the outcome of a generalisation which I previously made [1] in connection with the solution of certain difference equations. Only formal theorems are considered here. For a discussion of convergence reference may be made to the works [2, 3, 4, 5] cited at the end. The paper by Paley and XJrsell is particularly important since these authors discuss very fully the non-cyclic simple continued fraction

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 3 , February 1933 , pp. 189 - 200
Copyright
Copyright © Edinburgh Mathematical Society 1933

References

REFERENCES

1.Milne-Thomson., L. M.—On the operational solution of the homogeneous linear equation of finite differences by generalised continued fractions. Proc. Royal Soc. Edinburgh, 51 (1931), 91.CrossRefGoogle Scholar
2.MaunSell., F. G.—Some notes on extended continued fractions. Proc. London Math. Soc. (2), 30 (1929), 127.Google Scholar
3.Paley, R. E. A. C. and Ursell., H. D.—Continued fractions in several dimensions. Proc. Cambridge Phil. Soc, 26(1930), 127.CrossRefGoogle Scholar
4.Perron, O..—Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmiis. Math. Ann., 64 (1907), 1.CrossRefGoogle Scholar
5.Perron, O..—Die Konvergenz der Jacobi-Kettenalgorithmen mit komplexen Elementen. Stxsber. Ahad. München, 37 (1907).Google Scholar