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Continuants and precontinuants

Published online by Cambridge University Press:  24 October 2008

G. T. Bennett
G. T. Bennett
Affiliation:
Emmanuel CollegeCambridge
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Extract

1. It is here expedient to ignore the continued fractions from which they are usually derived and to define the simple continuants determined by the parameters a1, a2, a3, …, an, … as given by the chain of difference equations

together with the initial values u0 = 0, u1 = 1: and these data lead successively to the functions

and

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 35 , Issue 4 , November 1939 , pp. 548 - 561
Copyright
Copyright © Cambridge Philosophical Society 1939

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References

* Here and later where no ambiguity would arise the tabular continuant symbol [p, q] will be written in the attenuated form pq. The empty square brackets are reminders of the omission.