Some aspects of simultaneous rational approximation
Marcel G. de-Bruin (1990)
Banach Center Publications
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Some aspects of simultaneous rational approximation
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D. H. Fowler (1993)
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This article explores the use of the euclidian algorithm as a most useful way of handling ratios, especially when good rational approximations are required. Illustrations are taken from a discussion of the analysis of greek architecture by J.J Coulton. Although this is intended as a practical account, some discussions of theoretical aspects are included, and also of the relationship of this procedure to a new interpretation of early greek mathematics.
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Borwein, J., Crandall, R. (2004)
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Hurwitz continued fractions with confluent hypergeometric functions
Takao Komatsu (2007)
Czechoslovak Mathematical Journal
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Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.
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Denis, Remy Y. (1990)
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Simple Continued Fractions and Their Convergents
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Formalized Mathematics
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The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.