On a theorem of Legendre in the theory of continued fractions
Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Komatsu, Takao (2006)
Mathematica Pannonica
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Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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Takao Komatsu (2003)
Acta Arithmetica
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Boris Adamczewski (2010)
Acta Arithmetica
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James Mc Laughlin (2008)
Acta Arithmetica
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Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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Bo Li, Yan Zhang, Artur Korniłowicz (2006)
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.
Anton Lukyanenko, Joseph Vandehey (2015)
Acta Arithmetica
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We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
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.