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XIII.—On the Operational Solution of the Homogeneous Linear Equation of Finite Differences by Generalised Continued Fractions

Published online by Cambridge University Press:  15 September 2014

L. M. Milne-Thomson
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Summary

The homogeneous linear equation of the second order may be solved by means of a, continued fraction whose elements are coefficients in the equation. The two dimensional continued fraction is generalised to m dimensions and yields the solution of the equation of the mth order.

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Proceedings
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Proceedings of the Royal Society of Edinburgh , Volume 51 , 1932 , pp. 91 - 96
Copyright
Copyright © Royal Society of Edinburgh 1932

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References

page 92 note * Proc. Camb. Phil. Soc., 26, p. 127, 1930.

page 96 note * See Milne-Thomson, L. M., Proc. Camb. Phil. Soc., 27, p. 26, 1931CrossRefGoogle Scholar, where a general operational method, applicable to all linear equations with constant coefficients, is given. The above equation is here taken merely as the simplest illustration of the continued fraction method.