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A Theorem on Continued Fractions

Published online by Cambridge University Press:  20 January 2009

G. N. Watson
G. N. Watson
Affiliation:
46 Warwick New Road, Leamington, Warwickshire
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One of the outstanding theorems in the theory of continued fractions is the result described by O. Perron, Die Lehre von den Kettenbrüchen (1912, 1929, 1954–7) as the transformation of Bauer and Muir (for brevity I shall call it the BM theorem); this theorem and limiting cases of it give rise to numerous extremely interesting consequences.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 11 , Issue 3 , May 1959 , pp. 167 - 174
Copyright
Copyright © Edinburgh Mathematical Society 1959

References

BIBLIOGRAPHY

(1) Bauer, G., Abh. der k.b. Akad. der Wiss. zu München, 11 (1872), II.Google Scholar
(2) Muir, T., Phil. Mag. (5), 3 (1877), 137–138, 360–366.CrossRefGoogle Scholar
(3) Perron, O., Die Lehre von den Kettenbrüchen (1912, 1929, 1954–1957); see especially §§ 47 and 42 of the edition of 1929.Google Scholar