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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computer use in continued fraction expansions

Author: Evelyn Frank
Journal: Math. Comp. 23 (1969), 429-435
MathSciNet review: 0245509
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Abstract: In this study, the use of computers is demonstrated for the rapid expansion of a general regular continued fraction with rational elements for $ \surd C + L$, where $ C$ and $ L$ are rational numbers, $ C$ positive. Formulas for the expansion are derived. Conditions for the periodicity are considered. A Fortran program for the algorithms is given, as well as sample continued fraction expansions. Up to the present, practically all studies have been concerned with continued fractions with partial numerators $ \pm 1$ and partial denominators positive integers, due to difficulties in calculation. But now the use of computers makes possible the study of a much greater variety of continued fraction expansions.

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Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society