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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The parabola theorem for continued fractions over a vector space


Author: F. A. Roach
Journal: Proc. Amer. Math. Soc. 28 (1971), 137-146
MSC: Primary 40.12
MathSciNet review: 0275004
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Abstract: In a recent paper, we defined a type of reciprocal for points of a real inner product space and considered continued fractions based on this reciprocal. These continued fractions were analogous to ordinary continued fractions in which each partial numerator is unity. In the present paper, we develop a type of continued fraction which is analogous to an ordinary continued fraction of the form in which each partial denominator is unity. The main result is a convergence theorem for such continued fractions which is a direct extension of a theorem by W. T. Scott and H. S. Wall (the Parabola Theorem).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0275004-4
PII: S 0002-9939(1971)0275004-4
Keywords: Continued fractions
Article copyright: © Copyright 1971 American Mathematical Society