### A proof of the continued fraction expansion of ${e}^{2/s}$.

Komatsu, Takao (2007)

Integers

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Komatsu, Takao (2007)

Integers

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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.

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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Komatsu, Takao (2004)

Mathematica Pannonica

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Florin P. Boca, Joseph Vandehey (2012)

Acta Arithmetica

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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.

Komatsu, Takao (2006)

Mathematica Pannonica

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Denis, Remy Y. (1990)

International Journal of Mathematics and Mathematical Sciences

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J. Mc Laughlin, Nancy J. Wyshinski (2005)

Acta Arithmetica

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Boonrod Yuttanan (2012)

Acta Arithmetica

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S. G. Dani (2015)

Acta Arithmetica

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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...

Xue Hai Hu, Jun Wu (2009)

Acta Arithmetica

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