Computer use in continued fraction expansions
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- by Evelyn Frank PDF
- Math. Comp. 23 (1969), 429-435 Request permission
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.References
- Evelyn Frank, On continued fraction expansions for binomial quadratic surds, Numer. Math. 4 (1962), 85–95. MR 140181, DOI 10.1007/BF01386298
- Evelyn Frank, On continued fraction expansions for binomial quadratic surds. III, Numer. Math. 5 (1963), 113–117. MR 155421, DOI 10.1007/BF01385883
- Evelyn Frank, Continued fraction expansions with real numerical elements, Univ. Lisboa Rev. Fac. Ci. A (2) 12 (1967/68), 25–40. MR 246013
- Evelyn Frank, Continued fraction expansions with rational elements for binomial quadratic surds, Univ. Lisboa Rev. Fac. Ci. A (2) 12 (1967/68), 145–159 (1967/68). MR 247319
- J. Vicente Gonçalves, Sur le développement des irrationnalités quadratiques en fraction continue, Univ. Lisboa Rev. Fac. Ci. A (2) 4 (1955), 273–282 (French). MR 70670
- Oskar Perron, Die Lehre von den Kettenbrüchen. Bd I. Elementare Kettenbrüche, B. G. Teubner Verlagsgesellschaft, Stuttgart, 1954 (German). 3te Aufl. MR 0064172
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 429-435
- DOI: https://doi.org/10.1090/S0025-5718-69-99645-8
- MathSciNet review: 0245509